Switch to: References

Add citations

You must login to add citations.
  1. Weakly Compact Cardinals in Models of Set Theory.Ali Enayat - 1985 - Journal of Symbolic Logic 50 (2):476-486.
  • Models with Second Order Properties in Successors of Singulars.Rami Grossberg - 1989 - Journal of Symbolic Logic 54 (1):122-137.
    Let L(Q) be first order logic with Keisler's quantifier, in the λ + interpretation (= the satisfaction is defined as follows: $M \models (\mathbf{Q}x)\varphi(x)$ means there are λ + many elements in M satisfying the formula φ(x)). Theorem 1. Let λ be a singular cardinal; assume □ λ and GCH. If T is a complete theory in L(Q) of cardinality at most λ, and p is an L(Q) 1-type so that T strongly omits $p (= p$ has no support, to (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark  
  • Making the Hyperreal Line Both Saturated and Complete.H. Jerome Keisler & James H. Schmerl - 1991 - Journal of Symbolic Logic 56 (3):1016-1025.
    In a nonstandard universe, the $\kappa$-saturation property states that any family of fewer than $\kappa$ internal sets with the finite intersection property has a nonempty intersection. An ordered field $F$ is said to have the $\lambda$-Bolzano-Weierstrass property iff $F$ has cofinality $\lambda$ and every bounded $\lambda$-sequence in $F$ has a convergent $\lambda$-subsequence. We show that if $\kappa < \lambda$ are uncountable regular cardinals and $\beta^\alpha < \lambda$ whenever $\alpha < \kappa$ and $\beta < \lambda$, then there is a $\kappa$-saturated nonstandard (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  • The Consistency of ZFC + 2ℵ0 > ℵω + ℐ = ℐ.Martin Gilchrist & Saharon Shelah - 1997 - Journal of Symbolic Logic 62 (4):1151-1160.
  • Identities on Cardinals Less Than ℵω.M. Gilchrist & S. Shelah - 1996 - Journal of Symbolic Logic 61 (3):780 - 787.
  • Recursive Logic Frames.Saharon Shelah & Jouko Väänänen - 2006 - Mathematical Logic Quarterly 52 (2):151-164.
    We define the concept of a logic frame , which extends the concept of an abstract logic by adding the concept of a syntax and an axiom system. In a recursive logic frame the syntax and the set of axioms are recursively coded. A recursive logic frame is called complete , if every finite consistent theory has a model. We show that for logic frames built from the cardinality quantifiers “there exists at least λ ” completeness always implies .0-compactness. On (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  • On the Symbiosis Between Model-Theoretic and Set-Theoretic Properties of Large Cardinals.Joan Bagaria & Jouko Väänänen - 2016 - Journal of Symbolic Logic 81 (2):584-604.
  • Blunt and Topless End Extensions of Models of Set Theory.Matt Kaufmann - 1983 - Journal of Symbolic Logic 48 (4):1053-1073.
    Let U be a well-founded model of ZFC whose class of ordinals has uncountable cofinality, such that U has a Σ n end extension for each n ∈ ω. It is shown in Theorem 1.1 that there is such a model which has no elementary end extension. In the process some interesting facts about topless end extensions (those with no least new ordinal) are uncovered, for example Theorem 2.1: If U is a well-founded model of ZFC, such that U has (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  • Models with Second Order Properties V: A General Principle.Saharon Shelah, Claude Laflamme & Bradd Hart - 1993 - Annals of Pure and Applied Logic 64 (2):169-194.
    Shelah, S., C. Laflamme and B. Hart, Models with second order properties V: A general principle, Annals of Pure and Applied Logic 64 169–194. We present a general framework for carrying out the construction in [2-10] and others of the same type. The unifying factor is a combinatorial principle which we present in terms of a game in which the first player challenges the second player to carry out constructions which would be much easier in a generic extension of the (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  • Models with Second Order Properties IV. A General Method and Eliminating Diamonds.Saharon Shelah - 1983 - Annals of Pure and Applied Logic 25 (2):183-212.
    We show how to build various models of first-order theories, which also have properties like: tree with only definable branches, atomic Boolean algebras or ordered fields with only definable automorphisms. For this we use a set-theoretic assertion, which may be interesting by itself on the existence of quite generic subsets of suitable partial orders of power λ + , which follows from ♦ λ and even weaker hypotheses . For a related assertion, which is equivalent to the morass see Shelah (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  • Saturation and Simple Extensions of Models of Peano Arithmetic.Matt Kaufmann & James H. Schmerl - 1984 - Annals of Pure and Applied Logic 27 (2):109-136.
  • Remarks in Abstract Model Theory.Saharon Shelah - 1983 - Annals of Pure and Applied Logic 29 (3):255-288.
  • Filter Logics: Filters on Ω1.Matt Kaufmann - 1981 - Annals of Mathematical Logic 20 (2):155-200.
  • Models of Positive Truth.Mateusz Łełyk & Bartosz Wcisło - 2019 - Review of Symbolic Logic 12 (1):144-172.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  • Incomparable Ω1 -Like Models of Set Theory.Gunter Fuchs, Victoria Gitman & Joel David Hamkins - 2017 - Mathematical Logic Quarterly 63 (1-2):66-76.
    No categories
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  • Models of Weak Theories of Truth.Mateusz Łełyk & Bartosz Wcisło - 2017 - Archive for Mathematical Logic 56 (5-6):453-474.
    No categories
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • A Standard Model of Peano Arithmetic with No Conservative Elementary Extension.Ali Enayat - 2008 - Annals of Pure and Applied Logic 156 (2):308-318.
    The principal result of this paper answers a long-standing question in the model theory of arithmetic [R. Kossak, J. Schmerl, The Structure of Models of Peano Arithmetic, Oxford University Press, 2006, Question 7] by showing that there exists an uncountable arithmetically closed family of subsets of the set ω of natural numbers such that the expansion of the standard model of Peano arithmetic has no conservative elementary extension, i.e., for any elementary extension of , there is a subset of ω* (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  • Recursively Saturated Nonstandard Models of Arithmetic.C. Smoryński - 1981 - Journal of Symbolic Logic 46 (2):259-286.
  • The Bounded Proper Forcing Axiom.Martin Goldstern & Saharon Shelah - 1995 - Journal of Symbolic Logic 60 (1):58-73.
    The bounded proper forcing axiom BPFA is the statement that for any family of ℵ 1 many maximal antichains of a proper forcing notion, each of size ℵ 1 , there is a directed set meeting all these antichains. A regular cardinal κ is called Σ 1 -reflecting, if for any regular cardinal χ, for all formulas $\varphi, "H(\chi) \models`\varphi'"$ implies " $\exists\delta . We investigate several algebraic consequences of BPFA, and we show that the consistency strength of the bounded (...)
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   16 citations  
  • Conservative Extensions of Models of Set Theory and Generalizations.Ali Enayat - 1986 - Journal of Symbolic Logic 51 (4):1005-1021.
  • Power-Like Models of Set Theory.Ali Enayat - 2001 - Journal of Symbolic Logic 66 (4):1766-1782.
    A model M = (M, E,...) of Zermelo-Fraenkel set theory ZF is said to be θ-like, where E interprets ∈ and θ is an uncountable cardinal, if |M| = θ but $|\{b \in M: bEa\}| for each a ∈ M. An immediate corollary of the classical theorem of Keisler and Morley on elementary end extensions of models of set theory is that every consistent extension of ZF has an ℵ 1 -like model. Coupled with Chang's two cardinal theorem this implies (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   2 citations