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  1. Yoshihiro Abe (1985). Some Results Concerning Strongly Compact Cardinals. Journal of Symbolic Logic 50 (4):874-880.
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  2. Yoshihiro Abe (1984). Strongly Compact Cardinals, Elementary Embeddings and Fixed Points. Journal of Symbolic Logic 49 (3):808-812.
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  3. Alexander Abian (1978). Passages Between Finite and Infinite. Notre Dame Journal of Formal Logic 19 (3):452-456.
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  4. Alexander Abian & Wael A. Amin (1991). The Cardinality of Powersets in Finite Models of the Powerset Axiom. Notre Dame Journal of Formal Logic 32 (2):290-293.
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  5. Alexander Abian & Samuel LaMacchia (1978). On the Consistency and Independence of Some Set-Theoretical Axioms. Notre Dame Journal of Formal Logic 19 (1):155-158.
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  6. Alexander Abian & Samuel Lamacchia (1965). Some Consequences of the Axiom of Power-Set. Journal of Symbolic Logic 30 (3):293-294.
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  7. U. Abraham & S. Shelah (1986). On the Intersection of Closed Unbounded Sets. Journal of Symbolic Logic 51 (1):180-189.
    Forcing extensions yield models of ZFC in which a long sequence of club subsets of ω 1 has the following property: every subsequence of size ℵ 1 has a finite intersection.
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  8. Uri Abraham & Saharon Shelah (2004). Ladder Gaps Over Stationary Sets. Journal of Symbolic Logic 69 (2):518 - 532.
    For a stationary set $S \subseteq \omega_{1}$ and a ladder system C over S, a new type of gaps called C-Hausdorff is introduced and investigated. We describe a forcing model of ZFC in which, for some stationary set S, for every ladder C over S, every gap contains a subgap that is C-Hausdorff. But for every ladder E over \omega_{1} \ S$ there exists a gap with no subgap that is E-Hausdorff. A new type of chain condition, called polarized chain (...)
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  9. Uri Abraham & Saharon Shelah (2002). Coding with Ladders a Well Ordering of the Reals. Journal of Symbolic Logic 67 (2):579-597.
    Any model of ZFC + GCH has a generic extension (made with a poset of size ℵ 2 ) in which the following hold: MA + 2 ℵ 0 = ℵ 2 +there exists a Δ 2 1 -well ordering of the reals. The proof consists in iterating posets designed to change at will the guessing properties of ladder systems on ω 1 . Therefore, the study of such ladders is a main concern of this article.
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  10. Uri Abraham & Saharon Shelah (1983). Forcing Closed Unbounded Sets. Journal of Symbolic Logic 48 (3):643-657.
    We discuss the problem of finding forcing posets which introduce closed unbounded subsets to a given stationary set.
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  11. Amir D. Aczel (2000). The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity. Four Walls Eight Windows.
    From the end of the 19th century until his death, one of history's most brilliant mathematicians languished in an asylum. The Mystery of the Aleph tells the story of Georg Cantor (1845-1918), a Russian-born German who created set theory, the concept of infinite numbers, and the "continuum hypothesis," which challenged the very foundations of mathematics. His ideas brought expected denunciation from established corners - he was called a "corruptor of youth" not only for his work in mathematics, but for his (...)
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  12. Peter Aczel (2006). Aspects of General Topology in Constructive Set Theory. Annals of Pure and Applied Logic 137 (1):3-29.
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  13. Peter Aczel (1972). Describing Ordinals Using Functionals of Transfinite Type. Journal of Symbolic Logic 37 (1):35-47.
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  14. Peter Aczel, Laura Crosilla, Hajime Ishihara, Erik Palmgren & Peter Schuster (2006). Binary Refinement Implies Discrete Exponentiation. Studia Logica 84 (3):361 - 368.
    Working in the weakening of constructive Zermelo-Fraenkel set theory in which the subset collection scheme is omitted, we show that the binary re.nement principle implies all the instances of the exponentiation axiom in which the basis is a discrete set. In particular binary re.nement implies that the class of detachable subsets of a set form a set. Binary re.nement was originally extracted from the fullness axiom, an equivalent of subset collection, as a principle that was su.cient to prove that the (...)
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  15. Luca Alberucci & Vincenzo Salipante (2004). On Modal Μ-Calculus and Non-Well-Founded Set Theory. Journal of Philosophical Logic 33 (4):343-360.
    A finitary characterization for non-well-founded sets with finite transitive closure is established in terms of a greatest fixpoint formula of the modal μ-calculus. This generalizes the standard result in the literature where a finitary modal characterization is provided only for wellfounded sets with finite transitive closure. The proof relies on the concept of automaton, leading then to new interlinks between automata theory and non-well-founded sets.
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  16. Donald A. Alton (1971). Recursively Enumerable Sets Which Are Uniform for Finite Extensions. Journal of Symbolic Logic 36 (2):271-287.
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  17. P. V. Andreev & E. I. Gordon (2001). An Axiomatics for Nonstandard Set Theory, Based on Von Neumann-Bernays-Gödel Theory. Journal of Symbolic Logic 66 (3):1321-1341.
    We present an axiomatic framework for nonstandard analysis-the Nonstandard Class Theory (NCT) which extends von Neumann-Gödel-Bernays Set Theory (NBG) by adding a unary predicate symbol St to the language of NBG (St(X) means that the class X is standard) and axioms-related to it- analogs of Nelson's idealization, standardization and transfer principles. Those principles are formulated as axioms, rather than axiom schemes, so that NCT is finitely axiomatizable. NCT can be considered as a theory of definable classes of Bounded Set Theory (...)
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  18. Petr Andreev & Karel Hrbacek (2004). Standard Sets in Nonstandard Set Theory. Journal of Symbolic Logic 69 (1):165-182.
    We prove that Standardization fails in every nontrivial universe definable in the nonstandard set theory BST, and that a natural characterization of the standard universe is both consistent with and independent of BST. As a consequence we obtain a formulation of nonstandard class theory in the ∈-language.
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  19. H. Andréka, I. Hodkinson & I. Németi (1999). Finite Algebras of Relations Are Representable on Finite Sets. Journal of Symbolic Logic 64 (1):243-267.
    Using a combinatorial theorem of Herwig on extending partial isomorphisms of relational structures, we give a simple proof that certain classes of algebras, including Crs, polyadic Crs, and WA, have the `finite base property' and have decidable universal theories, and that any finite algebra in each class is representable on a finite set.
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  20. Simon Andrews (2010). Definable Open Sets As Finite Unions of Definable Open Cells. Notre Dame Journal of Formal Logic 51 (2):247-251.
    We introduce CE- cell decomposition , a modified version of the usual o-minimal cell decomposition. We show that if an o-minimal structure $\mathcal{R}$ admits CE-cell decomposition then any definable open set in $\mathcal{R}$ may be expressed as a finite union of definable open cells. The dense linear ordering and linear o-minimal expansions of ordered abelian groups are examples of such structures.
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  21. Irving H. Anellis (1993). Letters: The Philosophy of Set Theory by Mary Tiles Oxford: Blackwell, 1989. Philosophia Mathematica 1 (1):71-73.
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  22. Irving H. Anellis (1987). Russell's Earliest Interpretation of Cantorian Set Theory, 1896–1900. Philosophia Mathematica (1):1-31.
  23. G. Aldo Antonelli (1999). Free Set Algebras Satisfying Systems of Equations. Journal of Symbolic Logic 64 (4):1656-1674.
    In this paper we introduce the notion of a set algebra S satisfying a system E of equations. After defining a notion of freeness for such algebras, we show that, for any system E of equations, set algebras that are free in the class of structures satisfying E exist and are unique up to a bisimulation. Along the way, analogues of classical set-theoretic and algebraic properties are investigated.
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  24. Gian Aldo Antonelli (1994). Non-Well-Founded Sets Via Revision Rules. Journal of Philosophical Logic 23 (6):633 - 679.
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  25. K. I. Appel (1967). There Exist Two Regressive Sets Whose Intersection is Not Regressive. Journal of Symbolic Logic 32 (3):322-324.
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  26. Charles H. Applebaum (1973). A Stronger Definition of a Recursively Infinite Set. Notre Dame Journal of Formal Logic 14 (3):411-412.
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  27. Arthur W. Apter (2001). Supercompactness and Measurable Limits of Strong Cardinals. Journal of Symbolic Logic 66 (2):629-639.
    In this paper, two theorems concerning measurable limits of strong cardinals and supercompactness are proven. This generalizes earlier work, both individual and joint with Shelah.
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  28. Arthur W. Apter (2001). Some Structural Results Concerning Supercompact Cardinals. Journal of Symbolic Logic 66 (4):1919-1927.
    We show how the forcing of [5] can be iterated so as to get a model containing supercompact cardinals in which every measurable cardinal δ is δ + supercompact. We then apply this iteration to prove three additional theorems concerning the structure of the class of supercompact cardinals.
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  29. Arthur W. Apter (1999). On Measurable Limits of Compact Cardinals. Journal of Symbolic Logic 64 (4):1675-1688.
    We extend earlier work (both individual and joint with Shelah) and prove three theorems about the class of measurable limits of compact cardinals, where a compact cardinal is one which is either strongly compact or supercompact. In particular, we construct two models in which every measurable limit of compact cardinals below the least supercompact limit of supercompact cardinals possesses non-trivial degrees of supercompactness. In one of these models, every measurable limit of compact cardinals is a limit of supercompact cardinals and (...)
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  30. Arthur W. Apter (1999). On the Consistency Strength of Two Choiceless Cardinal Patterns. Notre Dame Journal of Formal Logic 40 (3):341-345.
    Using work of Devlin and Schindler in conjunction with work on Prikry forcing in a choiceless context done by the author, we show that two choiceless cardinal patterns have consistency strength of at least one Woodin cardinal.
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  31. Arthur W. Apter (1998). Laver Indestructibility and the Class of Compact Cardinals. Journal of Symbolic Logic 63 (1):149-157.
    Using an idea developed in joint work with Shelah, we show how to redefine Laver's notion of forcing making a supercompact cardinal κ indestructible under κ-directed closed forcing to give a new proof of the Kimchi-Magidor Theorem in which every compact cardinal in the universe (supercompact or strongly compact) satisfies certain indestructibility properties. Specifically, we show that if K is the class of supercompact cardinals in the ground model, then it is possible to force and construct a generic extension in (...)
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  32. Arthur W. Apter (1996). Ad and Patterns of Singular Cardinals Below Θ. Journal of Symbolic Logic 61 (1):225-235.
    Using Steel's recent result that assuming AD, in L[R] below Θ, κ is regular $\operatorname{iff} \kappa$ is measurable, we mimic below Θ certain earlier results of Gitik. In particular, we construct via forcing a model in which all uncountable cardinals below Θ are singular and a model in which the only regular uncountable cardinal below Θ is ℵ 1.
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  33. Arthur W. Apter (1990). Successors of Singular Cardinals and Measurability Revisited. Journal of Symbolic Logic 55 (2):492-501.
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  34. Arthur W. Apter & James Cummings (2002). Blowing Up the Power Set of the Least Measurable. Journal of Symbolic Logic 67 (3):915-923.
    We prove some results related to the problem of blowing up the power set of the least measurable cardinal. Our forcing results improve those of [1] by using the optimal hypothesis.
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  35. Arthur W. Apter & James Cummings (2000). Identity Crises and Strong Compactness. Journal of Symbolic Logic 65 (4):1895-1910.
    Combining techniques of the first author and Shelah with ideas of Magidor, we show how to get a model in which, for fixed but arbitrary finite n, the first n strongly compact cardinals κ 1 ,..., κ n are so that κ i for i = 1,..., n is both the i th measurable cardinal and κ + i supercompact. This generalizes an unpublished theorem of Magidor and answers a question of Apter and Shelah.
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  36. Arthur W. Apter & Moti Gitik (1998). The Least Measurable Can Be Strongly Compact and Indestructible. Journal of Symbolic Logic 63 (4):1404-1412.
    We show the consistency, relative to a supercompact cardinal, of the least measurable cardinal being both strongly compact and fully Laver indestructible. We also show the consistency, relative to a supercompact cardinal, of the least strongly compact cardinal being somewhat supercompact yet not completely supercompact and having both its strong compactness and degree of supercompactness fully Laver indestructible.
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  37. Arthur W. Apter & Joel David Hamkins (2003). Exactly Controlling the Non-Supercompact Strongly Compact Cardinals. Journal of Symbolic Logic 68 (2):669-688.
    We summarize the known methods of producing a non-supercompact strongly compact cardinal and describe some new variants. Our Main Theorem shows how to apply these methods to many cardinals simultaneously and exactly control which cardinals are supercompact and which are only strongly compact in a forcing extension. Depending upon the method, the surviving non-supercompact strongly compact cardinals can be strong cardinals, have trivial Mitchell rank or even contain a club disjoint from the set of measurable cardinals. These results improve and (...)
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  38. Arthur W. Apter & Joel David Hamkins (2002). Indestructibility and the Level-by-Level Agreement Between Strong Compactness and Supercompactness. Journal of Symbolic Logic 67 (2):820-840.
    Can a supercompact cardinal κ be Laver indestructible when there is a level-by-level agreement between strong compactness and supercompactness? In this article, we show that if there is a sufficiently large cardinal above κ, then no, it cannot. Conversely, if one weakens the requirement either by demanding less indestructibility, such as requiring only indestructibility by stratified posets, or less level-by-level agreement, such as requiring it only on measure one sets, then yes, it can.
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  39. Arthur W. Apter & James M. Henle (1986). Large Cardinal Structures Below ℵω. Journal of Symbolic Logic 51 (3):591 - 603.
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  40. Arthur W. Apter & Peter Koepke (2010). The Consistency Strength of Choiceless Failures of SCH. Journal of Symbolic Logic 75 (3):1066-1080.
    We determine exact consistency strengths for various failures of the Singular Cardinals Hypothesis (SCH) in the setting of the Zermelo-Fraenkel axiom system ZF without the Axiom of Choice (AC). By the new notion of parallel Prikry forcing that we introduce, we obtain surjective failures of SCH using only one measurable cardinal, including a surjective failure of Shelah's pcf theorem about the size of the power set of $\aleph _{\omega}$ . Using symmetric collapses to $\aleph _{\omega}$ , $\aleph _{\omega _{1}}$ , (...)
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  41. Jonas Rafael Becker Arenhart (2011). A Discussion on Finite Quasi-Cardinals in Quasi-Set Theory. Foundations of Physics 41 (8):1338-1354.
    Quasi-set theory Q is an alternative set-theory designed to deal mathematically with collections of indistinguishable objects. The intended interpretation for those objects is the indistinguishable particles of non-relativistic quantum mechanics, under one specific interpretation of that theory. The notion of cardinal of a collection in Q is treated by the concept of quasi-cardinal, which in the usual formulations of the theory is introduced as a primitive symbol, since the usual means of cardinal definition fail for collections of indistinguishable objects. In (...)
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  42. F. G. Asenjo (1970). Generalized Reals. Notre Dame Journal of Formal Logic 11 (4):473-476.
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  43. F. G. Asenjo (1967). Rings of Term-Relation Numbers as Non-Standard Models. Notre Dame Journal of Formal Logic 8 (1-2):24-26.
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  44. F. G. Asenjo (1963). Relations Irreducible to Classes. Notre Dame Journal of Formal Logic 4 (3):193-200.
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  45. Jeremy Avigad (2010). Proof Theory. Gödel and the Metamathematical Tradition. In Kurt Gödel, Solomon Feferman, Charles Parsons & Stephen G. Simpson (eds.), Kurt Gödel: Essays for His Centennial. Association for Symbolic Logic.
  46. Jeremy Avigad (2000). Interpreting Classical Theories in Constructive Ones. Journal of Symbolic Logic 65 (4):1785-1812.
    A number of classical theories are interpreted in analogous theories that are based on intuitionistic logic. The classical theories considered include subsystems of first- and second-order arithmetic, bounded arithmetic, and admissible set theory.
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  47. A. Avron & B. Konikowska (2008). Rough Sets and 3-Valued Logics. Studia Logica 90 (1):69 - 92.
    In the paper we explore the idea of describing Pawlak’s rough sets using three-valued logic, whereby the value t corresponds to the positive region of a set, the value f — to the negative region, and the undefined value u — to the border of the set. Due to the properties of the above regions in rough set theory, the semantics of the logic is described using a non-deterministic matrix (Nmatrix). With the strong semantics, where only the value t is (...)
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  48. Arnon Avron, A New Approach to Predicative Set Theory.
    We suggest a new framework for the Weyl-Feferman predicativist program by constructing a formal predicative set theory P ZF which resembles ZF , and is suitable for mechanization. The basic idea is that the predicatively acceptable instances of the comprehension schema are those which determine the collections they define in an absolute way, independent of the extension of the “surrounding universe”. The language of P ZF is type-free, and it reflects real mathematical practice in making an extensive use of statically (...)
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  49. Arnon Avron, Constructibility and Decidability Versus Domain Independence and Absoluteness.
    We develop a unified framework for dealing with constructibility and absoluteness in set theory, decidability of relations in effective structures (like the natural numbers), and domain independence of queries in database theory. Our framework and results suggest that domain-independence and absoluteness might be the key notions in a general theory of constructibility, predicativity, and computability.
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  50. S. Awodey, N. Gambino & M. A. Warren (2009). Lawvere-Tierney Sheaves in Algebraic Set Theory. Journal of Symbolic Logic 74 (3):861 - 890.
    We present a solution to the problem of defining a counterpart in Algebraic Set Theory of the construction of internal sheaves in Topos Theory. Our approach is general in that we consider sheaves as determined by Lawvere-Tierney coverages, rather than by Grothendieck coverages, and assume only a weakening of the axioms for small maps originally introduced by Joyal and Moerdijk, thus subsuming the existing topos-theoretic results.
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