Switch to: References

Citations of:

[Omnibus Review]

Journal of Symbolic Logic 57 (1):261-262 (1992)

Add citations

You must login to add citations.
  1. Mental representation.Hartry Field - 1978 - Erkenntnis 13 (July):9-61.
    Download  
     
    Export citation  
     
    Bookmark   289 citations  
  • God meets Satan’s Apple: the paradox of creation.Rubio Daniel - 2018 - Philosophical Studies 175 (12):2987-3004.
    It is now the majority view amongst philosophers and theologians that any world could have been better. This places the choice of which world to create into an especially challenging class of decision problems: those that are discontinuous in the limit. I argue that combining some weak, plausible norms governing this type of problem with a creator who has the attributes of the god of classical theism results in a paradox: no world is possible. After exploring some ways out of (...)
    Download  
     
    Export citation  
     
    Bookmark   17 citations  
  • What Are Structural Properties?†.Johannes Korbmacher & Georg Schiemer - 2018 - Philosophia Mathematica 26 (3):295-323.
    Informally, structural properties of mathematical objects are usually characterized in one of two ways: either as properties expressible purely in terms of the primitive relations of mathematical theories, or as the properties that hold of all structurally similar mathematical objects. We present two formal explications corresponding to these two informal characterizations of structural properties. Based on this, we discuss the relation between the two explications. As will be shown, the two characterizations do not determine the same class of mathematical properties. (...)
    Download  
     
    Export citation  
     
    Bookmark   18 citations  
  • The Iterative Conception of Set: a (Bi-)Modal Axiomatisation.J. P. Studd - 2013 - Journal of Philosophical Logic 42 (5):1-29.
    The use of tensed language and the metaphor of set ‘formation’ found in informal descriptions of the iterative conception of set are seldom taken at all seriously. Both are eliminated in the nonmodal stage theories that formalise this account. To avoid the paradoxes, such accounts deny the Maximality thesis, the compelling thesis that any sets can form a set. This paper seeks to save the Maximality thesis by taking the tense more seriously than has been customary (although not literally). A (...)
    Download  
     
    Export citation  
     
    Bookmark   43 citations  
  • Does category theory provide a framework for mathematical structuralism?Geoffrey Hellman - 2003 - Philosophia Mathematica 11 (2):129-157.
    Category theory and topos theory have been seen as providing a structuralist framework for mathematics autonomous vis-a-vis set theory. It is argued here that these theories require a background logic of relations and substantive assumptions addressing mathematical existence of categories themselves. We propose a synthesis of Bell's many-topoi view and modal-structuralism. Surprisingly, a combination of mereology and plural quantification suffices to describe hypothetical large domains, recovering the Grothendieck method of universes. Both topos theory and set theory can be carried out (...)
    Download  
     
    Export citation  
     
    Bookmark   60 citations  
  • Fundamentality from grounding trees.Fabrice Correia - 2021 - Synthese 199 (3-4):5965-5994.
    I provide and defend two natural accounts of fundamentality for facts that do justice to the idea that the “degree of fundamentality” enjoyed by a fact is a matter of how far, from a ground-theoretic perspective, the fact is from the ungrounded facts.
    Download  
     
    Export citation  
     
    Bookmark   8 citations  
  • Forcing and the Universe of Sets: Must We Lose Insight?Neil Barton - 2020 - Journal of Philosophical Logic 49 (4):575-612.
    A central area of current philosophical debate in the foundations of mathematics concerns whether or not there is a single, maximal, universe of set theory. Universists maintain that there is such a universe, while Multiversists argue that there are many universes, no one of which is ontologically privileged. Often forcing constructions that add subsets to models are cited as evidence in favour of the latter. This paper informs this debate by analysing ways the Universist might interpret this discourse that seems (...)
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  • What is the theory without power set?Victoria Gitman, Joel David Hamkins & Thomas A. Johnstone - 2016 - Mathematical Logic Quarterly 62 (4-5):391-406.
    We show that the theory, consisting of the usual axioms of but with the power set axiom removed—specifically axiomatized by extensionality, foundation, pairing, union, infinity, separation, replacement and the assertion that every set can be well‐ordered—is weaker than commonly supposed and is inadequate to establish several basic facts often desired in its context. For example, there are models of in which ω1 is singular, in which every set of reals is countable, yet ω1 exists, in which there are sets of (...)
    Download  
     
    Export citation  
     
    Bookmark   19 citations  
  • Set mapping reflection.Justin Tatch Moore - 2005 - Journal of Mathematical Logic 5 (1):87-97.
    In this note we will discuss a new reflection principle which follows from the Proper Forcing Axiom. The immediate purpose will be to prove that the bounded form of the Proper Forcing Axiom implies both that 2ω = ω2 and that [Formula: see text] satisfies the Axiom of Choice. It will also be demonstrated that this reflection principle implies that □ fails for all regular κ > ω1.
    Download  
     
    Export citation  
     
    Bookmark   35 citations  
  • Axiomatic Theories of Partial Ground II: Partial Ground and Hierarchies of Typed Truth.Johannes Korbmacher - 2018 - Journal of Philosophical Logic 47 (2):193-226.
    This is part two of a two-part paper in which we develop an axiomatic theory of the relation of partial ground. The main novelty of the paper is the of use of a binary ground predicate rather than an operator to formalize ground. In this part of the paper, we extend the base theory of the first part of the paper with hierarchically typed truth-predicates and principles about the interaction of partial ground and truth. We show that our theory is (...)
    Download  
     
    Export citation  
     
    Bookmark   8 citations  
  • Logically Simple Properties and Relations.Jan Plate - 2016 - Philosophers' Imprint 16:1-40.
    This paper presents an account of what it is for a property or relation (or ‘attribute’ for short) to be logically simple. Based on this account, it is shown, among other things, that the logically simple attributes are in at least one important way sparse. This in turn lends support to the view that the concept of a logically simple attribute can be regarded as a promising substitute for Lewis’s concept of a perfectly natural attribute. At least in part, the (...)
    Download  
     
    Export citation  
     
    Bookmark   8 citations  
  • C(n)-cardinals.Joan Bagaria - 2012 - Archive for Mathematical Logic 51 (3-4):213-240.
    For each natural number n, let C(n) be the closed and unbounded proper class of ordinals α such that Vα is a Σn elementary substructure of V. We say that κ is a C(n)-cardinal if it is the critical point of an elementary embedding j : V → M, M transitive, with j(κ) in C(n). By analyzing the notion of C(n)-cardinal at various levels of the usual hierarchy of large cardinal principles we show that, starting at the level of superstrong (...)
    Download  
     
    Export citation  
     
    Bookmark   19 citations  
  • Forcing with quotients.Michael Hrušák & Jindřich Zapletal - 2008 - Archive for Mathematical Logic 47 (7-8):719-739.
    We study an extensive connection between quotient forcings of Borel subsets of Polish spaces modulo a σ-ideal and quotient forcings of subsets of countable sets modulo an ideal.
    Download  
     
    Export citation  
     
    Bookmark   18 citations  
  • The logic of comparative cardinality.Yifeng Ding, Matthew Harrison-Trainor & Wesley H. Holliday - 2020 - Journal of Symbolic Logic 85 (3):972-1005.
    This paper investigates the principles that one must add to Boolean algebra to capture reasoning not only about intersection, union, and complementation of sets, but also about the relative size of sets. We completely axiomatize such reasoning under the Cantorian definition of relative size in terms of injections.
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  • The mathematical development of set theory from Cantor to Cohen.Akihiro Kanamori - 1996 - Bulletin of Symbolic Logic 2 (1):1-71.
    Set theory is an autonomous and sophisticated field of mathematics, enormously successful not only at its continuing development of its historical heritage but also at analyzing mathematical propositions cast in set-theoretic terms and gauging their consistency strength. But set theory is also distinguished by having begun intertwined with pronounced metaphysical attitudes, and these have even been regarded as crucial by some of its great developers. This has encouraged the exaggeration of crises in foundations and of metaphysical doctrines in general. However, (...)
    Download  
     
    Export citation  
     
    Bookmark   19 citations  
  • Ramsey-like cardinals.Victoria Gitman - 2011 - Journal of Symbolic Logic 76 (2):519 - 540.
    One of the numerous characterizations of a Ramsey cardinal κ involves the existence of certain types of elementary embeddings for transitive sets of size κ satisfying a large fragment of ZFC. We introduce new large cardinal axioms generalizing the Ramsey elementary embeddings characterization and show that they form a natural hierarchy between weakly compact cardinals and measurable cardinals. These new axioms serve to further our knowledge about the elementary embedding properties of smaller large cardinals, in particular those still consistent with (...)
    Download  
     
    Export citation  
     
    Bookmark   14 citations  
  • Matrix iterations and Cichon’s diagram.Diego Alejandro Mejía - 2013 - Archive for Mathematical Logic 52 (3-4):261-278.
    Using matrix iterations of ccc posets, we prove the consistency with ZFC of some cases where the cardinals on the right hand side of Cichon’s diagram take two or three arbitrary values (two regular values, the third one with uncountable cofinality). Also, mixing this with the techniques in J Symb Log 56(3):795–810, 1991, we can prove that it is consistent with ZFC to assign, at the same time, several arbitrary regular values on the left hand side of Cichon’s diagram.
    Download  
     
    Export citation  
     
    Bookmark   12 citations  
  • Fragility and indestructibility of the tree property.Spencer Unger - 2012 - Archive for Mathematical Logic 51 (5-6):635-645.
    We prove various theorems about the preservation and destruction of the tree property at ω2. Working in a model of Mitchell [9] where the tree property holds at ω2, we prove that ω2 still has the tree property after ccc forcing of size \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\aleph_1}$$\end{document} or adding an arbitrary number of Cohen reals. We show that there is a relatively mild forcing in this same model which destroys the tree property. Finally we (...)
    Download  
     
    Export citation  
     
    Bookmark   13 citations  
  • Underdetermination of infinitesimal probabilities.Alexander R. Pruss - 2018 - Synthese 198 (1):777-799.
    A number of philosophers have attempted to solve the problem of null-probability possible events in Bayesian epistemology by proposing that there are infinitesimal probabilities. Hájek and Easwaran have argued that because there is no way to specify a particular hyperreal extension of the real numbers, solutions to the regularity problem involving infinitesimals, or at least hyperreal infinitesimals, involve an unsatisfactory ineffability or arbitrariness. The arguments depend on the alleged impossibility of picking out a particular hyperreal extension of the real numbers (...)
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  • Generalizations of the Kunen inconsistency.Joel David Hamkins, Greg Kirmayer & Norman Lewis Perlmutter - 2012 - Annals of Pure and Applied Logic 163 (12):1872-1890.
    We present several generalizations of the well-known Kunen inconsistency that there is no nontrivial elementary embedding from the set-theoretic universe V to itself. For example, there is no elementary embedding from the universe V to a set-forcing extension V[G], or conversely from V[G] to V, or more generally from one set-forcing ground model of the universe to another, or between any two models that are eventually stationary correct, or from V to HOD, or conversely from HOD to V, or indeed (...)
    Download  
     
    Export citation  
     
    Bookmark   12 citations  
  • A Groszek‐Laver pair of undistinguishable ‐classes.Mohammad Golshani, Vladimir Kanovei & Vassily Lyubetsky - 2017 - Mathematical Logic Quarterly 63 (1-2):19-31.
    A generic extension of the constructible universe by reals is defined, in which the union of ‐classes of x and y is a lightface set, but neither of these two ‐classes is separately ordinal‐definable.
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  • Abstract elementary classes and accessible categories.Tibor Beke & Jirí Rosický - 2012 - Annals of Pure and Applied Logic 163 (12):2008-2017.
    We investigate properties of accessible categories with directed colimits and their relationship with categories arising from ShelahʼsElementary Classes. We also investigate ranks of objects in accessible categories, and the effect of accessible functors on ranks.
    Download  
     
    Export citation  
     
    Bookmark   11 citations  
  • Countable Additivity, Idealization, and Conceptual Realism.Yang Liu - 2020 - Economics and Philosophy 36 (1):127-147.
    This paper addresses the issue of finite versus countable additivity in Bayesian probability and decision theory -- in particular, Savage's theory of subjective expected utility and personal probability. I show that Savage's reason for not requiring countable additivity in his theory is inconclusive. The assessment leads to an analysis of various highly idealised assumptions commonly adopted in Bayesian theory, where I argue that a healthy dose of, what I call, conceptual realism is often helpful in understanding the interpretational value of (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • Richness and Reflection.Neil Barton - 2016 - Philosophia Mathematica 24 (3):330-359.
    A pervasive thought in contemporary philosophy of mathematics is that in order to justify reflection principles, one must hold universism: the view that there is a single universe of pure sets. I challenge this kind of reasoning by contrasting universism with a Zermelian form of multiversism. I argue that if extant justifications of reflection principles using notions of richness are acceptable for the universist, then the Zermelian can use similar justifications. However, I note that for some forms of richness argument, (...)
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  • Forcing indestructibility of MAD families.Jörg Brendle & Shunsuke Yatabe - 2005 - Annals of Pure and Applied Logic 132 (2):271-312.
    Let A[ω]ω be a maximal almost disjoint family and assume P is a forcing notion. Say A is P-indestructible if A is still maximal in any P-generic extension. We investigate P-indestructibility for several classical forcing notions P. In particular, we provide a combinatorial characterization of P-indestructibility and, assuming a fragment of MA, we construct maximal almost disjoint families which are P-indestructible yet Q-destructible for several pairs of forcing notions . We close with a detailed investigation of iterated Sacks indestructibility.
    Download  
     
    Export citation  
     
    Bookmark   15 citations  
  • Models of weak theories of truth.Mateusz Łełyk & Bartosz Wcisło - 2017 - Archive for Mathematical Logic 56 (5):453-474.
    In the following paper we propose a model-theoretical way of comparing the “strength” of various truth theories which are conservative over $$ PA $$. Let $${\mathfrak {Th}}$$ denote the class of models of $$ PA $$ which admit an expansion to a model of theory $${ Th}$$. We show (combining some well known results and original ideas) that $$\begin{aligned} {{\mathfrak {PA}}}\supset {\mathfrak {TB}}\supset {{\mathfrak {RS}}}\supset {\mathfrak {UTB}}\supseteq \mathfrak {CT^-}, \end{aligned}$$ where $${\mathfrak {PA}}$$ denotes simply the class of all models of (...)
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  • Pointwise definable models of set theory.Joel David Hamkins, David Linetsky & Jonas Reitz - 2013 - Journal of Symbolic Logic 78 (1):139-156.
    A pointwise definable model is one in which every object is \loos definable without parameters. In a model of set theory, this property strengthens $V=\HOD$, but is not first-order expressible. Nevertheless, if \ZFC\ is consistent, then there are continuum many pointwise definable models of \ZFC. If there is a transitive model of \ZFC, then there are continuum many pointwise definable transitive models of \ZFC. What is more, every countable model of \ZFC\ has a class forcing extension that is pointwise definable. (...)
    Download  
     
    Export citation  
     
    Bookmark   9 citations  
  • Stacking mice.Ronald Jensen, Ernest Schimmerling, Ralf Schindler & John Steel - 2009 - Journal of Symbolic Logic 74 (1):315-335.
    We show that either of the following hypotheses imply that there is an inner model with a proper class of strong cardinals and a proper class of Woodin cardinals. 1) There is a countably closed cardinal k ≥ N₃ such that □k and □(k) fail. 2) There is a cardinal k such that k is weakly compact in the generic extension by Col(k, k⁺). Of special interest is 1) with k = N₃ since it follows from PFA by theorems of (...)
    Download  
     
    Export citation  
     
    Bookmark   12 citations  
  • The effective theory of Borel equivalence relations.Ekaterina B. Fokina, Sy-David Friedman & Asger Törnquist - 2010 - Annals of Pure and Applied Logic 161 (7):837-850.
    The study of Borel equivalence relations under Borel reducibility has developed into an important area of descriptive set theory. The dichotomies of Silver [20] and Harrington, Kechris and Louveau [6] show that with respect to Borel reducibility, any Borel equivalence relation strictly above equality on ω is above equality on , the power set of ω, and any Borel equivalence relation strictly above equality on the reals is above equality modulo finite on . In this article we examine the effective (...)
    Download  
     
    Export citation  
     
    Bookmark   11 citations  
  • From hierarchies to well-foundedness.Dandolo Flumini & Kentaro Sato - 2014 - Archive for Mathematical Logic 53 (7-8):855-863.
    We highlight that the connection of well-foundedness and recursive definitions is more than just convenience. While the consequences of making well-foundedness a sufficient condition for the existence of hierarchies have been extensively studied, we point out that well-foundedness is a necessary condition for the existence of hierarchies e.g. that even in an intuitionistic setting α⊢wfwhereα\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${_\alpha \vdash \mathsf{wf}\, {\rm where}\, _\alpha}$$\end{document} stands for the iteration of Π10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} (...)
    Download  
     
    Export citation  
     
    Bookmark   8 citations  
  • A definable E 0 class containing no definable elements.Vladimir Kanovei & Vassily Lyubetsky - 2015 - Archive for Mathematical Logic 54 (5-6):711-723.
    A generic extension L[x]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{L}[x]}$$\end{document} by a real x is defined, in which the E0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{E}_0}$$\end{document}-class of x is a lightface Π21\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\it \Pi}^1_2}$$\end{document} set containing no ordinal-definable reals.
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  • Projective wellorders and mad families with large continuum.Vera Fischer, Sy David Friedman & Lyubomyr Zdomskyy - 2011 - Annals of Pure and Applied Logic 162 (11):853-862.
    We show that is consistent with the existence of a -definable wellorder of the reals and a -definable ω-mad subfamily of [ω]ω.
    Download  
     
    Export citation  
     
    Bookmark   9 citations  
  • Forking in short and tame abstract elementary classes.Will Boney & Rami Grossberg - 2017 - Annals of Pure and Applied Logic 168 (8):1517-1551.
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  • Relations between some cardinals in the absence of the axiom of choice.Lorenz Halbeisen & Saharon Shelah - 2001 - Bulletin of Symbolic Logic 7 (2):237-261.
    If we assume the axiom of choice, then every two cardinal numbers are comparable, In the absence of the axiom of choice, this is no longer so. For a few cardinalities related to an arbitrary infinite set, we will give all the possible relationships between them, where possible means that the relationship is consistent with the axioms of set theory. Further we investigate the relationships between some other cardinal numbers in specific permutation models and give some results provable without using (...)
    Download  
     
    Export citation  
     
    Bookmark   12 citations  
  • Foundational implications of the inner model hypothesis.Tatiana Arrigoni & Sy-David Friedman - 2012 - Annals of Pure and Applied Logic 163 (10):1360-1366.
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  • Identity, indiscernibility, and philosophical claims.Décio Krause & Antonio Mariano Nogueira Coelho - 2005 - Axiomathes 15 (2):191-210.
    The concept of indiscernibility in a structure is analysed with the aim of emphasizing that in asserting that two objects are indiscernible, it is useful to consider these objects as members of (the domain of) a structure. A case for this usefulness is presented by examining the consequences of this view to the philosophical discussion on identity and indiscernibility in quantum theory.
    Download  
     
    Export citation  
     
    Bookmark   10 citations  
  • Random World and Quantum Mechanics.Jerzy Król, Krzysztof Bielas & Torsten Asselmeyer-Maluga - 2023 - Foundations of Science 28 (2):575-625.
    Quantum mechanics (QM) predicts probabilities on the fundamental level which are, via Born probability law, connected to the formal randomness of infinite sequences of QM outcomes. Recently it has been shown that QM is algorithmic 1-random in the sense of Martin–Löf. We extend this result and demonstrate that QM is algorithmic $$\omega$$ -random and generic, precisely as described by the ’miniaturisation’ of the Solovay forcing to arithmetic. This is extended further to the result that QM becomes Zermelo–Fraenkel Solovay random on (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Nothing But Gold. Complexities in Terms of Non-difference and Identity: Part 1. Coreferential Puzzles.Alberto Anrò - 2021 - Journal of Indian Philosophy 49 (3):361-386.
    Beginning from some passages by Vācaspati Miśra and Bhāskararāya Makhin discussing the relationship between a crown and the gold of which it is made, this paper investigates the complex underlying connections among difference, non-difference, coreferentiality, and qualification qua relations. Methodologically, philological care is paired with formal logical analysis on the basis of ‘Navya-Nyāya Formal Language’ premises and an axiomatic set theory-based approach. This study is intended as the first step of a broader investigation dedicated to analysing causation and transformation in (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • Large cardinals and definable well-orders on the universe.Andrew D. Brooke-Taylor - 2009 - Journal of Symbolic Logic 74 (2):641-654.
    We use a reverse Easton forcing iteration to obtain a universe with a definable well-order, while preserving the GCH and proper classes of a variety of very large cardinals. This is achieved by coding using the principle ◊ $_{k^ - }^* $ at a proper class of cardinals k. By choosing the cardinals at which coding occurs sufficiently sparsely, we are able to lift the embeddings witnessing the large cardinal properties without having to meet any non-trivial master conditions.
    Download  
     
    Export citation  
     
    Bookmark   8 citations  
  • Typed lambda-calculus in classical Zermelo-Frænkel set theory.Jean-Louis Krivine - 2001 - Archive for Mathematical Logic 40 (3):189-205.
    , which uses the intuitionistic propositional calculus, with the only connective →. It is very important, because the well known Curry-Howard correspondence between proofs and programs was originally discovered with it, and because it enjoys the normalization property: every typed term is strongly normalizable. It was extended to second order intuitionistic logic, in 1970, by J.-Y. Girard [4], under the name of system F, still with the normalization property.More recently, in 1990, the Curry-Howard correspondence was extended to classical logic, following (...)
    Download  
     
    Export citation  
     
    Bookmark   9 citations  
  • Unbounded families and the cofinality of the infinite symmetric group.James D. Sharp & Simon Thomas - 1995 - Archive for Mathematical Logic 34 (1):33-45.
    In this paper, we study the relationship between the cofinalityc(Sym(ω)) of the infinite symmetric group and the minimal cardinality $$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{b} $$ of an unbounded familyF of ω ω.
    Download  
     
    Export citation  
     
    Bookmark   9 citations  
  • Counterexamples to countable-section Π 2 1 uniformization and Π 3 1 separation.Vladimir Kanovei & Vassily Lyubetsky - 2016 - Annals of Pure and Applied Logic 167 (3):262-283.
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Martin’s conjecture and strong ergodicity.Simon Thomas - 2009 - Archive for Mathematical Logic 48 (8):749-759.
    In this paper, we explore some of the consequences of Martin’s Conjecture on degree invariant Borel maps. These include the strongest conceivable ergodicity result for the Turing equivalence relation with respect to the filter on the degrees generated by the cones, as well as the statement that the complexity of a weakly universal countable Borel equivalence relation always concentrates on a null set.
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  • Indestructibility of Vopěnka’s Principle.Andrew D. Brooke-Taylor - 2011 - Archive for Mathematical Logic 50 (5-6):515-529.
    Vopěnka’s Principle is a natural large cardinal axiom that has recently found applications in category theory and algebraic topology. We show that Vopěnka’s Principle and Vopěnka cardinals are relatively consistent with a broad range of other principles known to be independent of standard (ZFC) set theory, such as the Generalised Continuum Hypothesis, and the existence of a definable well-order on the universe of all sets. We achieve this by showing that they are indestructible under a broad class of forcing constructions, (...)
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  • The Bristol model: An abyss called a Cohen real.Asaf Karagila - 2018 - Journal of Mathematical Logic 18 (2):1850008.
    We construct a model [Formula: see text] of [Formula: see text] which lies between [Formula: see text] and [Formula: see text] for a Cohen real [Formula: see text] and does not have the form [Formula: see text] for any set [Formula: see text]. This is loosely based on the unwritten work done in a Bristol workshop about Woodin’s HOD Conjecture in 2011. The construction given here allows for a finer analysis of the needed assumptions on the ground models, thus taking (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • Forcing with finite conditions.Gregor Dolinar & Mirna Džamonja - 2013 - Annals of Pure and Applied Logic 164 (1):49-64.
    We give a construction of the square principle by means of forcing with finite conditions.
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  • Cardinal characteristics, projective wellorders and large continuum.Vera Fischer, Sy David Friedman & Lyubomyr Zdomskyy - 2013 - Annals of Pure and Applied Logic 164 (7-8):763-770.
    We extend the work of Fischer et al. [6] by presenting a method for controlling cardinal characteristics in the presence of a projective wellorder and 2ℵ0>ℵ2. This also answers a question of Harrington [9] by showing that the existence of a Δ31 wellorder of the reals is consistent with Martinʼs axiom and 2ℵ0=ℵ3.
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  • A minimal Prikry-type forcing for singularizing a measurable cardinal.Peter Koepke, Karen Räsch & Philipp Schlicht - 2013 - Journal of Symbolic Logic 78 (1):85-100.
    Recently, Gitik, Kanovei and the first author proved that for a classical Prikry forcing extension the family of the intermediate models can be parametrized by $\mathscr{P}(\omega)/\mathrm{finite}$. By modifying the standard Prikry tree forcing we define a Prikry-type forcing which also singularizes a measurable cardinal but which is minimal, i.e., there are \emph{no} intermediate models properly between the ground model and the generic extension. The proof relies on combining the rigidity of the tree structure with indiscernibility arguments resulting from the normality (...)
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  • Antichains of perfect and splitting trees.Paul Hein & Otmar Spinas - 2020 - Archive for Mathematical Logic 59 (3-4):367-388.
    We investigate uncountable maximal antichains of perfect trees and of splitting trees. We show that in the case of perfect trees they must have size of at least the dominating number, whereas for splitting trees they are of size at least \\), i.e. the covering coefficient of the meager ideal. Finally, we show that uncountable maximal antichains of superperfect trees are at least of size the bounding number; moreover we show that this is best possible.
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • Quantum Mechanics, Formalization and the Cosmological Constant Problem.Jerzy Król & Torsten Asselmeyer-Maluga - 2020 - Foundations of Science 25 (4):879-904.
    Based on formal arguments from Zermelo–Fraenkel set theory we develop the environment for explaining and resolving certain fundamental problems in physics. By these formal tools we show that any quantum system defined by an infinite dimensional Hilbert space of states interferes with the spacetime structure M. M and the quantum system both gain additional degrees of freedom, given by models of Zermelo–Fraenkel set theory. In particular, M develops the ground state where classical gravity vanishes. Quantum mechanics distinguishes set-theoretic random forcing (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations