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  1. Effectively closed sets and enumerations.Paul Brodhead & Douglas Cenzer - 2008 - Archive for Mathematical Logic 46 (7-8):565-582.
    An effectively closed set, or ${\Pi^{0}_{1}}$ class, may viewed as the set of infinite paths through a computable tree. A numbering, or enumeration, is a map from ω onto a countable collection of objects. One numbering is reducible to another if equality holds after the second is composed with a computable function. Many commonly used numberings of ${\Pi^{0}_{1}}$ classes are shown to be mutually reducible via a computable permutation. Computable injective numberings are given for the family of ${\Pi^{0}_{1}}$ classes and (...)
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  • Epistemic optimism.Mihai Ganea - 2008 - Philosophia Mathematica 16 (3):333-353.
    Michael Dummett's argument for intuitionism can be criticized for the implicit reliance on the existence of what might be called absolutely undecidable statements. Neil Tennant attacks epistemic optimism, the view that there are no such statements. I expose what seem serious flaws in his attack, and I suggest a way of defending the use of classical logic in arithmetic that circumvents the issue of optimism. I would like to thank an anonymous referee for helpful comments. CiteULike Connotea Del.icio.us What's this?
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  • Primitive recursive ordinal functions with added constants.Stanley H. Stahl - 1977 - Journal of Symbolic Logic 42 (1):77-82.
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  • Justification as truth-finding efficiency: How ockham's razor works.Kevin T. Kelly - 2004 - Minds and Machines 14 (4):485-505.
    I propose that empirical procedures, like computational procedures, are justified in terms of truth-finding efficiency. I contrast the idea with more standard philosophies of science and illustrate it by deriving Ockham's razor from the aim of minimizing dramatic changes of opinion en route to the truth.
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  • A contextual–hierarchical approach to truth and the liar paradox.Michael Glanzberg - 2004 - Journal of Philosophical Logic 33 (1):27-88.
    This paper presents an approach to truth and the Liar paradox which combines elements of context dependence and hierarchy. This approach is developed formally, using the techniques of model theory in admissible sets. Special attention is paid to showing how starting with some ideas about context drawn from linguistics and philosophy of language, we can see the Liar sentence to be context dependent. Once this context dependence is properly understood, it is argued, a hierarchical structure emerges which is neither ad (...)
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  • A Spector-Gandy theorem for cPC d () classes.Shaughan Lavine - 1992 - Journal of Symbolic Logic 57 (2):478-500.
    Let U be an admissible structure. A cPCd(U) class is the class of all models of a sentence of the form $\neg\exists\bar{K} \bigwedge \Phi$ , where K̄ is an U-r.e. set of relation symbols and φ is an U-r.e. set of formulas of L∞ω that are in U. The main theorem is a generalization of the following: Let U be a pure countable resolvable admissible structure such that U is not Σ-elementarily embedded in HYP(U). Then a class K of countable (...)
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  • The Constructive Hilbert Program and the Limits of Martin-Löf Type Theory.Michael Rathjen - 2005 - Synthese 147 (1):81-120.
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  • Theories and Ordinals in Proof Theory.Michael Rathjen - 2006 - Synthese 148 (3):719-743.
    How do ordinals measure the strength and computational power of formal theories? This paper is concerned with the connection between ordinal representation systems and theories established in ordinal analyses. It focusses on results which explain the nature of this connection in terms of semantical and computational notions from model theory, set theory, and generalized recursion theory.
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  • The computable testability of theories making uncomputable predictions.Kevin T. Kelly & Oliver Schulte - 1995 - Erkenntnis 43 (1):29 - 66.
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  • Possible-worlds semantics for modal notions conceived as predicates.Volker Halbach, Hannes Leitgeb & Philip Welch - 2003 - Journal of Philosophical Logic 32 (2):179-223.
    If □ is conceived as an operator, i.e., an expression that gives applied to a formula another formula, the expressive power of the language is severely restricted when compared to a language where □ is conceived as a predicate, i.e., an expression that yields a formula if it is applied to a term. This consideration favours the predicate approach. The predicate view, however, is threatened mainly by two problems: Some obvious predicate systems are inconsistent, and possible-worlds semantics for predicates of (...)
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  • On the relation between choice and comprehension principles in second order arithmetic.Andrea Cantini - 1986 - Journal of Symbolic Logic 51 (2):360-373.
    We give a new elementary proof of the comparison theorem relating $\sum^1_{n + 1}-\mathrm{AC}\uparrow$ and $\Pi^1_n -\mathrm{CA}\uparrow$ ; the proof does not use Skolem theories. By the same method we prove: a) $\sum^1_{n + 1}-\mathrm{DC} \uparrow \equiv (\Pi^1_n -CA)_{ , for suitable classes of sentences; b) $\sum^1_{n+1}-DC \uparrow$ proves the consistency of (Π 1 n -CA) ω k, for finite k, and hence is stronger than $\sum^1_{n+1}-AC \uparrow$ . a) and b) answer a question of Feferman and Sieg.
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  • Notes on Formal Theories of Truth.Andrea Cantini - 1989 - Mathematical Logic Quarterly 35 (2):97-130.
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  • Relative predicativity and dependent recursion in second-order set theory and higher-order theories.Sato Kentaro - 2014 - Journal of Symbolic Logic 79 (3):712-732.
    This article reports that some robustness of the notions of predicativity and of autonomous progression is broken down if as the given infinite total entity we choose some mathematical entities other than the traditionalω. Namely, the equivalence between normal transfinite recursion scheme and newdependent transfinite recursionscheme, which does hold in the context of subsystems of second order number theory, does not hold in the context of subsystems of second order set theory where the universeVof sets is treated as the given (...)
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  • Universal functions in partial structures.Maurizio Negri - 1992 - Mathematical Logic Quarterly 38 (1):253-268.
    In this work we show that every structure [MATHEMATICAL SCRIPT CAPITAL A] can be expanded to a partial structure [MATHEMATICAL SCRIPT CAPITAL A]* with universal functions for the class of polynomials on [MATHEMATICAL SCRIPT CAPITAL A]*. We can embed [MATHEMATICAL SCRIPT CAPITAL A]* monomorphically in a total structure [MATHEMATICAL SCRIPT CAPITAL A]º that preserves universal functions of [MATHEMATICAL SCRIPT CAPITAL A]* and that is universal among such structures, i.e. [MATHEMATICAL SCRIPT CAPITAL A]º can be homomorphically embedded in every total structure (...)
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  • Binary Relations Over the Category of Enumerated Sets.A. Orlicki - 1988 - Mathematical Logic Quarterly 34 (3):265-276.
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  • Real computation with least discrete advice: A complexity theory of nonuniform computability with applications to effective linear algebra.Martin Ziegler - 2012 - Annals of Pure and Applied Logic 163 (8):1108-1139.
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  • Some Reflections on the Foundations of Ordinary Recursion Theory and a New Proposal.George Tourlakis - 1986 - Mathematical Logic Quarterly 32 (31-34):503-515.
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  • Recursion in Partial Type‐1 Objects With Well‐Behaved Oracles.George Tourlakis - 1996 - Mathematical Logic Quarterly 42 (1):449-460.
    We refine the definition of II-computability of [12] so that oracles have a “consistent”, but natural, behaviour. We prove a Kleene Normal Form Theorem and closure of semi-recursive relations under ∃1. We also show that in this more inclusive computation theory Post's theorem in the arithmetical hierarchy still holds.
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  • Physics of brain-mind interaction.John C. Eccles - 1990 - Behavioral and Brain Sciences 13 (4):662-663.
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  • The realm of primitive recursion.Harold Simmons - 1988 - Archive for Mathematical Logic 27 (2):177-188.
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  • Ptykes in GödelsT und Definierbarkeit von Ordinalzahlen.Peter Päppinghaus - 1989 - Archive for Mathematical Logic 28 (2):119-141.
    We prove two of the inequalities needed to obtain the following result on the ordinal values of ptykes of type 2, which are definable in Gödel'sT. LetG be a dilator satisfyingG(0)=ω, ∀x:G(x)≧x, and ∀η<Ω:G(η)<Ω, and letg be the ordinal function induced byG. Then sup{A(G)∣A ptyx of type 2 definable in Gödel'sT} = sup{x∣x is∑ 1 g -definable without parameters provably in KP(G)} =J (2 +Id) g (ω) (0) = the “Bachmann-Howard ordinal relative tog”. KP(G) is obtained from Kripke-Platek set theory (...)
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  • Bounds on Scott rank for various nonelementary classes.David Marker - 1990 - Archive for Mathematical Logic 30 (2):73-82.
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  • Monotone inductive definitions over the continuum.Douglas Cenzer - 1976 - Journal of Symbolic Logic 41 (1):188-198.
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  • Cores of Π11 sets of reals.Andreas Blass & Douglas Cenzer - 1974 - Journal of Symbolic Logic 39 (4):649 - 654.
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  • Discrete transfinite computation models.Philip D. Welch - 2011 - In S. B. Cooper & Andrea Sorbi (eds.), Computability in Context: Computation and Logic in the Real World. World Scientific. pp. 375--414.
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