29 found
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  1. New Constructions of Satisfaction Classes.Albert Visser & Ali Enayat - 2015 - In Kentaro Fujimoto, José Martínez Fernández, Henri Galinon & Theodora Achourioti (eds.), Unifying the Philosophy of Truth. Springer Verlag.
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  2.  20
    Truth and Feasible Reducibility.Ali Enayat, Mateusz Łełyk & Bartosz Wcisło - 2020 - Journal of Symbolic Logic 85 (1):367-421.
    Let ${\cal T}$ be any of the three canonical truth theories CT^− (compositional truth without extra induction), FS^− (Friedman–Sheard truth without extra induction), or KF^− (Kripke–Feferman truth without extra induction), where the base theory of ${\cal T}$ is PA. We establish the following theorem, which implies that ${\cal T}$ has no more than polynomial speed-up over PA. Theorem.${\cal T}$is feasibly reducible to PA, in the sense that there is a polynomial time computable function f such that for every ${\cal T}$-proof (...)
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  3.  16
    Truth, Disjunction, and Induction.Ali Enayat & Fedor Pakhomov - 2019 - Archive for Mathematical Logic 58 (5-6):753-766.
    By a well-known result of Kotlarski et al., first-order Peano arithmetic \ can be conservatively extended to the theory \ of a truth predicate satisfying compositional axioms, i.e., axioms stating that the truth predicate is correct on atomic formulae and commutes with all the propositional connectives and quantifiers. This result motivates the general question of determining natural axioms concerning the truth predicate that can be added to \ while maintaining conservativity over \. Our main result shows that conservativity fails even (...)
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  4.  15
    Unifying the Model Theory of First-Order and Second-Order Arithmetic Via WKL0⁎.Ali Enayat & Tin Lok Wong - 2017 - Annals of Pure and Applied Logic 168 (6):1247-1283.
  5.  21
    Fixed Points of Self-Embeddings of Models of Arithmetic.Saeideh Bahrami & Ali Enayat - 2018 - Annals of Pure and Applied Logic 169 (6):487-513.
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  6.  13
    Iterated Ultrapowers for the Masses.Ali Enayat, Matt Kaufmann & Zachiri McKenzie - 2018 - Archive for Mathematical Logic 57 (5-6):557-576.
    We present a novel, perspicuous framework for building iterated ultrapowers. Furthermore, our framework naturally lends itself to the construction of a certain type of order indiscernibles, here dubbed tight indiscernibles, which are shown to provide smooth proofs of several results in general model theory.
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  7.  10
    Largest Initial Segments Pointwise Fixed by Automorphisms of Models of Set Theory.Ali Enayat, Matt Kaufmann & Zachiri McKenzie - 2018 - Archive for Mathematical Logic 57 (1-2):91-139.
    Given a model \ of set theory, and a nontrivial automorphism j of \, let \\) be the submodel of \ whose universe consists of elements m of \ such that \=x\) for every x in the transitive closure of m ). Here we study the class \ of structures of the form \\), where the ambient model \ satisfies a frugal yet robust fragment of \ known as \, and \=m\) whenever m is a finite ordinal in the sense (...)
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  8.  43
    Models of Set Theory with Definable Ordinals.Ali Enayat - 2005 - Archive for Mathematical Logic 44 (3):363-385.
    A DO model (here also referred to a Paris model) is a model of set theory all of whose ordinals are first order definable in . Jeffrey Paris (1973) initiated the study of DO models and showed that (1) every consistent extension T of ZF has a DO model, and (2) for complete extensions T, T has a unique DO model up to isomorphism iff T proves V=OD. Here we provide a comprehensive treatment of Paris models. Our results include the (...)
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  9.  12
    Automorphisms of Models of Arithmetic: A Unified View.Ali Enayat - 2007 - Annals of Pure and Applied Logic 145 (1):16-36.
    We develop the method of iterated ultrapower representation to provide a unified and perspicuous approach for building automorphisms of countable recursively saturated models of Peano arithmetic . In particular, we use this method to prove Theorem A below, which confirms a long-standing conjecture of James Schmerl.Theorem AIf is a countable recursively saturated model of in which is a strong cut, then for any there is an automorphism j of such that the fixed point set of j is isomorphic to .We (...)
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  10.  5
    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* (...)
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  11.  37
    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 (...)
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  12.  71
    Leibnizian Models of Set Theory.Ali Enayat - 2004 - Journal of Symbolic Logic 69 (3):775-789.
    A model is said to be Leibnizian if it has no pair of indiscernibles. Mycielski has shown that there is a first order axiom LM (the Leibniz-Mycielski axiom) such that for any completion T of Zermelo-Fraenkel set theory ZF, T has a Leibnizian model if and only if T proves LM. Here we prove: THEOREM A. Every complete theory T extending ZF + LM has $2^{\aleph_{0}}$ nonisomorphic countable Leibnizian models. THEOREM B. If $\kappa$ is aprescribed definable infinite cardinal of a (...)
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  13.  44
    Model Theory of the Regularity and Reflection Schemes.Ali Enayat & Shahram Mohsenipour - 2008 - Archive for Mathematical Logic 47 (5):447-464.
    This paper develops the model theory of ordered structures that satisfy Keisler’s regularity scheme and its strengthening REF ${(\mathcal{L})}$ (the reflection scheme) which is an analogue of the reflection principle of Zermelo-Fraenkel set theory. Here ${\mathcal{L}}$ is a language with a distinguished linear order <, and REF ${(\mathcal {L})}$ consists of formulas of the form $$\exists x \forall y_{1} < x \ldots \forall y_{n} < x \varphi (y_{1},\ldots ,y_{n})\leftrightarrow \varphi^{ < x}(y_1, \ldots ,y_n),$$ where φ is an ${\mathcal{L}}$ -formula, φ (...))
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  14.  8
    Marginalia on a Theorem of Woodin.Rasmus Blanck & Ali Enayat - 2017 - Journal of Symbolic Logic 82 (1):359-374.
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  15.  2
    Zfc Proves That the Class of Ordinals is Not Weakly Compact for Definable Classes.Ali Enayat & Joel David Hamkins - 2018 - Journal of Symbolic Logic 83 (1):146-164.
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  16.  3
    End Extending Models of Set Theory Via Power Admissible Covers.Zachiri McKenzie & Ali Enayat - 2022 - Annals of Pure and Applied Logic 173 (8):103132.
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  17.  45
    Weakly Compact Cardinals in Models of Set Theory.Ali Enayat - 1985 - Journal of Symbolic Logic 50 (2):476-486.
  18. Manteghe Riazi.M. Ardeshir & Ali Enayat - 2008 - Bulletin of Symbolic Logic 14 (1):118-119.
     
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  19. Initial Self-Embeddings of Models of Set Theory.Ali Enayat & Zachiri Mckenzie - 2021 - Journal of Symbolic Logic 86 (4):1584-1611.
    By a classical theorem of Harvey Friedman, every countable nonstandard model $\mathcal {M}$ of a sufficiently strong fragment of ZF has a proper rank-initial self-embedding j, i.e., j is a self-embedding of $\mathcal {M}$ such that $j[\mathcal {M}]\subsetneq \mathcal {M}$, and the ordinal rank of each member of $j[\mathcal {M}]$ is less than the ordinal rank of each element of $\mathcal {M}\setminus j[\mathcal {M}]$. Here, we investigate the larger family of proper initial-embeddings j of models $\mathcal {M}$ of fragments of (...)
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  20.  4
    An Unpublished Theorem of Solovay on OD Partitions of Reals Into Two Non-OD Parts, Revisited.Ali Enayat & Vladimir Kanovei - 2020 - Journal of Mathematical Logic 21 (3):2150014.
    A definable pair of disjoint non-OD sets of reals exists in the Sacks and ????0-large generic extensions of the constructible universe L. More specifically, if a∈2ω is eith...
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  21.  25
    Minimal Elementary Extensions of Models of Set Theory and Arithmetic.Ali Enayat - 1990 - Archive for Mathematical Logic 30 (3):181-192.
    TheoremEvery model of ZFChas a conservative elementary extension which possesses a cofinal minimal elementary extension.An application of Boolean ultrapowers to models of full arithmetic is also presented.
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  22.  17
    Preface.Ali Enayat & Iraj Kalantari - 2010 - Annals of Pure and Applied Logic 161 (6):709-710.
  23.  16
    The First Iranian Summer School in Logic.Ali Enayat - 1993 - Journal of Symbolic Logic 58 (4):1476.
  24.  12
    Trees and Keislers Problem.Ali Enayat - 2001 - Archive for Mathematical Logic 40 (4):273-276.
    We give a new negative solution to Keisler's problem regarding Skolem functions and elementary extensions. In contrast to existing ad hoc solutions due to Payne, Knight, and Lachlan, our solution uses well-known models.
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  25. Marriott Wardman Park Hotel, Washington, DC January 7–8, 2009.Barbara F. Csima, Inessa Epstein, Rahim Moosa, Christian Rosendal, Jouko Väänänen & Ali Enayat - 2009 - Bulletin of Symbolic Logic 15 (2).
     
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  26.  8
    Preface.Ali Enayat, Massoud Pourmahdian & Ralf Schindler - 2018 - Archive for Mathematical Logic 57 (1-2):1-2.
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  27.  8
    2008-2009 Winter Meeting of the Association for Symbolic Logic.Ali Enayat & Barbara F. Csima - 2009 - Bulletin of Symbolic Logic 15 (2):237.
  28.  2
    Condensable models of set theory.Ali Enayat - 2022 - Archive for Mathematical Logic 61 (3):299-315.
    A model \ of ZF is said to be condensable if \\prec _{\mathbb {L}_{{\mathcal {M}}}} {\mathcal {M}}\) for some “ordinal” \, where \:=,\in )^{{\mathcal {M}}}\) and \ is the set of formulae of the infinitary logic \ that appear in the well-founded part of \. The work of Barwise and Schlipf in the 1970s revealed the fact that every countable recursively saturated model of ZF is cofinally condensable \prec _{\mathbb {L}_{{\mathcal {M}}}}{\mathcal {M}}\) for an unbounded collection of \). Moreover, it (...)
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  29.  5
    Conservative Extensions of Models of Set Theory and Generalizations.Ali Enayat - 1986 - Journal of Symbolic Logic 51 (4):1005-1021.