Switch to: Citations

Add references

You must login to add references.
  1. Generic structures and simple theories.Z. Chatzidakis & A. Pillay - 1998 - Annals of Pure and Applied Logic 95 (1-3):71-92.
    We study structures equipped with generic predicates and/or automorphisms, and show that in many cases we obtain simple theories. We also show that a bounded PAC field is simple. 1998 Published by Elsevier Science B.V. All rights reserved.
    Download  
     
    Export citation  
     
    Bookmark   72 citations  
  • Theories without the tree property of the second kind.Artem Chernikov - 2014 - Annals of Pure and Applied Logic 165 (2):695-723.
    We initiate a systematic study of the class of theories without the tree property of the second kind — NTP2. Most importantly, we show: the burden is “sub-multiplicative” in arbitrary theories ; NTP2 is equivalent to the generalized Kimʼs lemma and to the boundedness of ist-weight; the dp-rank of a type in an arbitrary theory is witnessed by mutually indiscernible sequences of realizations of the type, after adding some parameters — so the dp-rank of a 1-type in any theory is (...)
    Download  
     
    Export citation  
     
    Bookmark   37 citations  
  • On model-theoretic tree properties.Artem Chernikov & Nicholas Ramsey - 2016 - Journal of Mathematical Logic 16 (2):1650009.
    We study model theoretic tree properties and their associated cardinal invariants. In particular, we obtain a quantitative refinement of Shelah’s theorem for countable theories, show that [Formula: see text] is always witnessed by a formula in a single variable and that weak [Formula: see text] is equivalent to [Formula: see text]. Besides, we give a characterization of [Formula: see text] via a version of independent amalgamation of types and apply this criterion to verify that some examples in the literature are (...)
    Download  
     
    Export citation  
     
    Bookmark   26 citations  
  • Laforte, G., see Downey, R.T. Arai, Z. Chatzidakis & A. Pillay - 1998 - Annals of Pure and Applied Logic 95 (1-3):287.
    Download  
     
    Export citation  
     
    Bookmark   37 citations  
  • On ◁∗-maximality.Mirna Džamonja & Saharon Shelah - 2004 - Annals of Pure and Applied Logic 125 (1-3):119-158.
    This paper investigates a connection between the semantic notion provided by the ordering * among theories in model theory and the syntactic SOPn hierarchy of Shelah. It introduces two properties which are natural extensions of this hierarchy, called SOP2 and SOP1. It is shown here that SOP3 implies SOP2 implies SOP1. In Shelah's article 229) it was shown that SOP3 implies *-maximality and we prove here that *-maximality in a model of GCH implies a property called SOP2″. It has been (...)
    Download  
     
    Export citation  
     
    Bookmark   32 citations  
  • Tree indiscernibilities, revisited.Byunghan Kim, Hyeung-Joon Kim & Lynn Scow - 2014 - Archive for Mathematical Logic 53 (1-2):211-232.
    We give definitions that distinguish between two notions of indiscernibility for a set {aη∣η∈ω>ω}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\{a_{\eta} \mid \eta \in ^{\omega>}\omega\}}$$\end{document} that saw original use in Shelah [Classification theory and the number of non-isomorphic models. North-Holland, Amsterdam, 1990], which we name s- and str−indiscernibility. Using these definitions and detailed proofs, we prove s- and str-modeling theorems and give applications of these theorems. In particular, we verify a step in the argument that TP is equivalent (...)
    Download  
     
    Export citation  
     
    Bookmark   15 citations  
  • On generic structures.D. W. Kueker & M. C. Laskowski - 1992 - Notre Dame Journal of Formal Logic 33 (2):175-183.
    Download  
     
    Export citation  
     
    Bookmark   22 citations  
  • Notions around tree property 1.Byunghan Kim & Hyeung-Joon Kim - 2011 - Annals of Pure and Applied Logic 162 (9):698-709.
    In this paper, we study the notions related to tree property 1 , or, equivalently, SOP2. Among others, we supply a type-counting criterion for TP1 and show the equivalence of TP1 and k- TP1. Then we introduce the notions of weak k- TP1 for k≥2, and also supply type-counting criteria for those. We do not know whether weak k- TP1 implies TP1, but at least we prove that each weak k- TP1 implies SOP1. Our generalization of the tree-indiscernibility results in (...)
    Download  
     
    Export citation  
     
    Bookmark   15 citations  
  • On the existence of indiscernible trees.Kota Takeuchi & Akito Tsuboi - 2012 - Annals of Pure and Applied Logic 163 (12):1891-1902.
    We introduce several concepts concerning the indiscernibility of trees. A tree is by definition an ordered set such that, for any a∈O, the initial segment {b∈O:b (...)
    Download  
     
    Export citation  
     
    Bookmark   11 citations  
  • Characterization of NIP theories by ordered graph-indiscernibles.Lynn Scow - 2012 - Annals of Pure and Applied Logic 163 (11):1624-1641.
    We generalize the Unstable Formula Theorem characterization of stable theories from Shelah [11], that a theory T is stable just in case any infinite indiscernible sequence in a model of T is an indiscernible set. We use a generalized form of indiscernibles from [11], in our notation, a sequence of parameters from an L-structure M, , indexed by an L′-structure I is L′-generalized indiscernible inM if qftpL′=qftpL′ implies tpL=tpL for all same-length, finite ¯,j from I. Let Tg be the theory (...)
    Download  
     
    Export citation  
     
    Bookmark   12 citations  
  • Indiscernibles, EM-Types, and Ramsey Classes of Trees.Lynn Scow - 2015 - Notre Dame Journal of Formal Logic 56 (3):429-447.
    The author has previously shown that for a certain class of structures $\mathcal {I}$, $\mathcal {I}$-indexed indiscernible sets have the modeling property just in case the age of $\mathcal {I}$ is a Ramsey class. We expand this known class of structures from ordered structures in a finite relational language to ordered, locally finite structures which isolate quantifier-free types by way of quantifier-free formulas. This result is applied to give new proofs that certain classes of trees are Ramsey. To aid this (...)
    Download  
     
    Export citation  
     
    Bookmark   9 citations  
  • Pseudo real closed fields, pseudo p-adically closed fields and NTP2.Samaria Montenegro - 2017 - Annals of Pure and Applied Logic 168 (1):191-232.
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  • Amalgamation of types in pseudo-algebraically closed fields and applications.Zoé Chatzidakis - 2019 - Journal of Mathematical Logic 19 (2):1950006.
    This paper studies unbounded pseudo-algebraically closed fields and shows an amalgamation result for types over algebraically closed sets. It discusses various applications, for instance that omega-free PAC fields have the property NSOP3. It also contains a description of imaginaries in PAC fields.
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  • Stability of nilpotent groups of class 2 and prime exponent.Alan H. Mekler - 1981 - Journal of Symbolic Logic 46 (4):781-788.
    Let p be an odd prime. A method is described which given a structure M of finite similarity type produces a nilpotent group of class 2 and exponent p which is in the same stability class as M. Theorem. There are nilpotent groups of class 2 and exponent p in all stability classes. Theorem. The problem of characterizing a stability class is equivalent to characterizing the (nilpotent, class 2, exponent p) groups in that class.
    Download  
     
    Export citation  
     
    Bookmark   14 citations  
  • A note on nsop1 in one variable.Nicholas Ramsey - 2019 - Journal of Symbolic Logic 84 (1):388-392.
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • Mekler's construction preserves CM-triviality.Andreas Baudisch - 2002 - Annals of Pure and Applied Logic 115 (1-3):115-173.
    For every structure M of finite signature Mekler 781) has constructed a group G such that for every κ the maximal number of n -types over an elementary equivalent model of cardinality κ is the same for M and G . These groups are nilpotent of class 2 and of exponent p , where p is a fixed prime greater than 2. We consider stable structures M only and show that M is CM -trivial if and only if G is (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations