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22J. A. Makowsky, Saharon Shelah, and Jonathan Stavi. ⊿-logics and generalized quantifiers. Annals of mathematical logic, vol. 10 , pp. 155–192 (review)Journal of Symbolic Logic 50 (1): 241-242. 1985.
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21A logic for arguing about probabilities in measure teamsArchive for Mathematical Logic 56 (5-6): 475-489. 2017.We use sets of assignments, a.k.a. teams, and measures on them to define probabilities of first-order formulas in given data. We then axiomatise first-order properties of such probabilities and prove a completeness theorem for our axiomatisation. We use the Hardy–Weinberg Principle of biology and the Bell’s Inequalities of quantum physics as examples.
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20K. Jon Barwise. Absolute logics and. Annals of mathematical logic, vol. 4 no. 3 , pp. 309–340Journal of Symbolic Logic 50 (1): 240-241. 1985.
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2023rd Workshop on Logic, Language, Information and ComputationLogic Journal of the IGPL 25 (2): 253-272. 2017.
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20Regular Ultrapowers at Regular CardinalsNotre Dame Journal of Formal Logic 56 (3): 417-428. 2015.In earlier work by the first and second authors, the equivalence of a finite square principle $\square^{\mathrm{fin}}_{\lambda,D}$ with various model-theoretic properties of structures of size $\lambda $ and regular ultrafilters was established. In this paper we investigate the principle $\square^{\mathrm{fin}}_{\lambda,D}$—and thereby the above model-theoretic properties—at a regular cardinal. By Chang’s two-cardinal theorem, $\square^{\mathrm{fin}}_{\lambda,D}$ holds at regular cardinals for a…Read more
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20Dependence logic in pregeometries and ω-stable theoriesJournal of Symbolic Logic 81 (1): 32-55. 2016.
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18Logicality and model classesBulletin of Symbolic Logic 27 (4): 385-414. 2021.We ask, when is a property of a model a logical property? According to the so-called Tarski–Sher criterion this is the case when the property is preserved by isomorphisms. We relate this to model-theoretic characteristics of abstract logics in which the model class is definable. This results in a graded concept of logicality in the terminology of Sagi [46]. We investigate which characteristics of logics, such as variants of the Löwenheim–Skolem theorem, Completeness theorem, and absoluteness, ar…Read more
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17Game-theoretic inductive definabilityAnnals of Pure and Applied Logic 65 (3): 265-306. 1993.Oikkonen, J. and J. Väänänen, Game-theoretic inductive definability, Annals of Pure and Applied Logic 65 265-306. We use game-theoretic ideas to define a generalization of the notion of inductive definability. This approach allows induction along non-well-founded trees. Our definition depends on an underlying partial ordering of the objects. In this ordering every countable ascending sequence is assumed to have a unique supremum which enables us to go over limits. We establish basic properties o…Read more
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16Reflection of Long Game FormulasMathematical Logic Quarterly 40 (3): 381-392. 1994.We study game formulas the truth of which is determined by a semantical game of uncountable length. The main theme is the study of principles stating reflection of these formulas in various admissible sets. This investigation leads to two weak forms of strict-II11 reflection . We show that admissible sets such as H and Lω2 which fail to have strict-II11 reflection, may or may not, depending on set-theoretic hypotheses satisfy one or both of these weaker forms
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15This book comprises revised full versions of lectures given during the 9th European Summer School in Logic, Languages, and Information, ESSLLI'97, held in Aix-en-Provence, France, in August 1997. The six lectures presented introduce the reader to the state of the art in the area of generalized quantifiers and computation. Besides an introductory survey by the volume editor various aspects of generalized quantifiers are studied in depth.
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1523rd Workshop on Logic, Language, Information and Computation - WoLLIC 2016Annals of Pure and Applied Logic 170 (9): 921-922. 2019.
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15Positional strategies in long ehrenfeucht–fraïssé gamesJournal of Symbolic Logic 80 (1): 285-300. 2015.
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14Finite information logicAnnals of Pure and Applied Logic 134 (1): 83-93. 2005.We introduce a generalization of Independence Friendly logic in which Eloise is restricted to a finite amount of information about Abelard’s moves. This logic is shown to be equivalent to a sublogic of first-order logic, to have the finite model property, and to be decidable. Moreover, it gives an exponential compression relative to logic
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14Boolean valued models and generalized quantifiersAnnals of Mathematical Logic 18 (3): 193-225. 1980.
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14
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13Review: J. A. Makowsky, Saharon Shelah, Jonathan Stavi, $Delta$-Logics and Generalized Quantifiers (review)Journal of Symbolic Logic 50 (1): 241-242. 1985.
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13An Overview of Saharon Shelah's Contributions to Mathematical Logic, in Particular to Model TheoryTheoria 87 (2): 349-360. 2020.I will give a brief overview of Saharon Shelah’s work in mathematical logic. I will focus on three transformative contributions Shelah has made: stability theory, proper forcing and PCF theory. The first is in model theory and the other two are in set theory.
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13Recursive logic framesMathematical Logic Quarterly 52 (2): 151-164. 2006.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 the other hand we show that a recursive…Read more
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12The hierarchy theorem for generalized quantifiersJournal of Symbolic Logic 61 (3): 802-817. 1996.The concept of a generalized quantifier of a given similarity type was defined in [12]. Our main result says that on finite structures different similarity types give rise to different classes of generalized quantifiers. More exactly, for every similarity typetthere is a generalized quantifier of typetwhich is not definable in the extension of first order logic by all generalized quantifiers of type smaller thant. This was proved for unary similarity types by Per Lindström [17] with a counting a…Read more
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11Decidability of Some Logics with Free Quantifier VariablesMathematical Logic Quarterly 27 (2‐6): 17-22. 1981.
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11Positive logicsArchive for Mathematical Logic 62 (1): 207-223. 2023.Lindström’s Theorem characterizes first order logic as the maximal logic satisfying the Compactness Theorem and the Downward Löwenheim-Skolem Theorem. If we do not assume that logics are closed under negation, there is an obvious extension of first order logic with the two model theoretic properties mentioned, namely existential second order logic. We show that existential second order logic has a whole family of proper extensions satisfying the Compactness Theorem and the Downward Löwenheim-Sko…Read more
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9Stationary Sets and Infinitary LogicJournal of Symbolic Logic 65 (3): 1311-1320. 2000.Let K$^0_\lambda$ be the class of structures $\langle\lambda,
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