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  1. The Role of Intuition in Gödel’s and Robinson’s Points of View.Talia Leven - 2019 - Axiomathes 29 (5):441-461.
    Before Abraham Robinson and Kurt Gödel became familiar with Paul Cohen’s Results, both logicians held a naïve Platonic approach to philosophy. In this paper I demonstrate how Cohen’s results influenced both of them. Robinson declared himself a Formalist, while Gödel basically continued to hold onto the old Platonic approach. Why were the reactions of Gödel and Robinson to Cohen’s results so drastically different in spite of the fact that their initial philosophical positions were remarkably similar? I claim that the key (...)
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  • Extensions of ordered theories by generic predicates.Alfred Dolich, Chris Miller & Charles Steinhorn - 2013 - Journal of Symbolic Logic 78 (2):369-387.
    Given a theoryTextending that of dense linear orders without endpoints, in a language ℒ ⊇ {<}, we are interested in extensionsT′ ofTin languages extending ℒ by unary relation symbols that are each interpreted in models ofT′ as sets that are both dense and codense in the underlying sets of the models.There is a canonically “wild” example, namelyT= Th andT′ = Th. Recall thatTis o-minimal, and so every open set definable in any model ofThas only finitely many definably connected components. But (...)
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  • Existentially closed structures.H. Simmons - 1972 - Journal of Symbolic Logic 37 (2):293-310.
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  • A counterexample in the theory of model companions.D. Saracino - 1975 - Journal of Symbolic Logic 40 (1):31-34.
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  • The word problem for division rings.Angus Macintyre - 1973 - Journal of Symbolic Logic 38 (3):428-436.
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  • Omitting quantifier-free types in generic structures.Angus Macintyre - 1972 - Journal of Symbolic Logic 37 (3):512-520.
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  • Step by step – Building representations in algebraic logic.Robin Hirsch & Ian Hodkinson - 1997 - Journal of Symbolic Logic 62 (1):225-279.
    We consider the problem of finding and classifying representations in algebraic logic. This is approached by letting two players build a representation using a game. Homogeneous and universal representations are characterized according to the outcome of certain games. The Lyndon conditions defining representable relation algebras (for the finite case) and a similar schema for cylindric algebras are derived. Finite relation algebras with homogeneous representations are characterized by first order formulas. Equivalence games are defined, and are used to establish whether an (...)
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  • Examples in the theory of existential completeness.Joram Hirschfeld - 1978 - Journal of Symbolic Logic 43 (4):650-658.
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  • Notions of relative ubiquity for invariant sets of relational structures.Paul Bankston & Wim Ruitenburg - 1990 - Journal of Symbolic Logic 55 (3):948-986.
    Given a finite lexicon L of relational symbols and equality, one may view the collection of all L-structures on the set of natural numbers ω as a space in several different ways. We consider it as: (i) the space of outcomes of certain infinite two-person games; (ii) a compact metric space; and (iii) a probability measure space. For each of these viewpoints, we can give a notion of relative ubiquity, or largeness, for invariant sets of structures on ω. For example, (...)
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  • Fields with several commuting derivations.David Pierce - 2014 - Journal of Symbolic Logic 79 (1):1-19.
    For every natural numberm, the existentially closed models of the theory of fields withmcommuting derivations can be given a first-order geometric characterization in several ways. In particular, the theory of these differential fields has a model-companion. The axioms are that certain differential varieties determined by certain ordinary varieties are nonempty. There is no restriction on the characteristic of the underlying field.
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  • The model-theoretic significance of complemented existential formulas.Volker Weispfenning - 1981 - Journal of Symbolic Logic 46 (4):843-850.
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  • An Application of Rank‐Forcing to ω 1 ‐Categoricity.H. Peter Tuschik - 1980 - Mathematical Logic Quarterly 26 (14-18):237-250.
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  • Iterated Admissibility Through Forcing in Strategic Belief Models.Fernando Tohmé, Gianluca Caterina & Jonathan Gangle - 2020 - Journal of Logic, Language and Information 29 (4):491-509.
    Iterated admissibility embodies a minimal criterion of rationality in interactions. The epistemic characterization of this solution has been actively investigated in recent times: it has been shown that strategies surviving \ rounds of iterated admissibility may be identified as those that are obtained under a condition called rationality and m assumption of rationality in complete lexicographic type structures. On the other hand, it has been shown that its limit condition, with an infinity assumption of rationality ), might not be satisfied (...)
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  • A generalized model companion for a theory of partially ordered fields.Werner Stegbauer - 1979 - Journal of Symbolic Logic 44 (4):643-652.
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  • On the notion of algebraic closedness for noncommutative groups and fields.Abraham Robinson - 1971 - Journal of Symbolic Logic 36 (3):441-444.
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  • Algebraically closed commutative local rings.K.-P. Podewski & Joachim Reineke - 1979 - Journal of Symbolic Logic 44 (1):89-94.
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  • An Application of Rank‐Forcing to ω 1 ‐Categoricity.H. Peter Tuschik - 1980 - Mathematical Logic Quarterly 26 (14-18):237-250.
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  • Forcing in Łukasiewicz Predicate Logic.Antonio Di Nola, George Georgescu & Luca Spada - 2008 - Studia Logica 89 (1):111-145.
    In this paper we study the notion of forcing for Łukasiewicz predicate logic (Ł∀, for short), along the lines of Robinson’s forcing in classical model theory. We deal with both finite and infinite forcing. As regard to the former we prove a Generic Model Theorem for Ł∀, while for the latter, we study the generic and existentially complete standard models of Ł∀.
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  • Model companions and k-model completeness for the complete theories of Boolean algebras.J. Mead & G. C. Nelson - 1980 - Journal of Symbolic Logic 45 (1):47-55.
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  • On countable locally described structures.Berthold J. Maier - 1987 - Annals of Pure and Applied Logic 35 (C):205-246.
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  • Quelques Proprietes des Enonces Universellement Forces.Jean-Claude Lablanquie - 1974 - Mathematical Logic Quarterly 20 (1‐3):31-36.
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  • Generic expansions of structures.Julia F. Knight - 1973 - Journal of Symbolic Logic 38 (4):561-570.
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  • Finite forcing, existential types and complete types.Joram Hirschfeld - 1980 - Journal of Symbolic Logic 45 (1):93-102.
    We use the spaces T n and E n of complete types and of existential types to investigate various notions which appear in the theory of the algebraic structure of models.
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  • Omitting types: Application to recursion theory.Thomas J. Grilliot - 1972 - Journal of Symbolic Logic 37 (1):81-89.
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  • Model theory for universal classes with the amalgamation property: A study in the foundations of model theory and algebra.William K. Forrest - 1977 - Annals of Mathematical Logic 11 (3):263.
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  • Model-completions and modules.P. Eklof - 1971 - Annals of Mathematical Logic 2 (3):251.
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  • Forcing in łukasiewicz predicate logic.Antonio Di Nola, George Georgescu & Luca Spada - 2008 - Studia Logica 89 (1):111-145.
    In this paper we study the notion of forcing for Łukasiewicz predicate logic (Ł∀, for short), along the lines of Robinson’s forcing in classical model theory. We deal with both finite and infinite forcing. As regard to the former we prove a Generic Model Theorem for Ł∀, while for the latter, we study the generic and existentially complete standard models of Ł∀.
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  • Model Theoretic Algebra.G. L. Cherlin - 1976 - Journal of Symbolic Logic 41 (2):537-545.
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  • Algebraically closed commutative rings.G. L. Cherlin - 1973 - Journal of Symbolic Logic 38 (3):493-499.
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  • Model-theoretic forcing in logic with a generalized quantifier.Kim B. Bruce - 1978 - Annals of Mathematical Logic 13 (3):225.
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  • The world, the flesh and the argument from design.William Boos - 1994 - Synthese 101 (1):15 - 52.
    In the the passage just quoted from theDialogues concerning Natural Religion, David Hume developed a thought-experiment that contravened his better-known views about chance expressed in hisTreatise and firstEnquiry.For among other consequences of the eternal-recurrence hypothesis Philo proposes in this passage, it may turn out that what the vulgar call cause is nothing but a secret and concealed chance.
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  • The world, the flesh and the argument from design.William Boos - 1995 - Synthese 104 (2):15 - 52.
    In the the passage just quoted from the Dialogues concerning Natural Religion, David Hume developed a thought-experiment that contravened his better-known views about "chance" expressed in his Treatise and first Enquiry. For among other consequences of the 'eternal-recurrence' hypothesis Philo proposes in this passage, it may turn out that what the vulgar call cause is nothing but a secret and concealed chance. (In this sentence, I have simply reversed "cause" and "chance" in a well-known passage from Hume's Treatise, p. 130). (...)
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  • Absolute logics and L∞ω.K. Jon Barwise - 1972 - Annals of Mathematical Logic 4 (3):309-340.
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  • Absolute logics and L∞ω.K. Jon Barwise - 1972 - Annals of Mathematical Logic 4 (3):309-340.
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