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14Boolean valued models and generalized quantifiersAnnals of Mathematical Logic 18 (3): 193-225. 1980.
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40Quantum Team Logic and Bell’s InequalitiesReview of Symbolic Logic 8 (4): 722-742. 2015.A logical approach to Bell's Inequalities of quantum mechanics has been introduced by Abramsky and Hardy [2]. We point out that the logical Bell's Inequalities of [2] are provable in the probability logic of Fagin, Halpern and Megiddo [4]. Since it is now considered empirically established that quantum mechanics violates Bell's Inequalities, we introduce a modified probability logic, that we call quantum team logic, in which Bell's Inequalities are not provable, and prove a Completeness Theorem …Read more
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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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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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15Positional strategies in long ehrenfeucht–fraïssé gamesJournal of Symbolic Logic 80 (1): 285-300. 2015.
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127From if to biSynthese 167 (2). 2009.We take a fresh look at the logics of informational dependence and independence of Hintikka and Sandu and Väänänen, and their compositional semantics due to Hodges. We show how Hodges’ semantics can be seen as a special case of a general construction, which provides a context for a useful completeness theorem with respect to a wider class of models. We shed some new light on each aspect of the logic. We show that the natural propositional logic carried by the semantics is the logic of Bunched Im…Read more
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18Game-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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114On the expressive power of monotone natural language quantifiers over finite modelsJournal of Philosophical Logic 31 (4): 327-358. 2002.We study definability in terms of monotone generalized quantifiers satisfying Isomorphism Closure, Conservativity and Extension. Among the quantifiers with the latter three properties - here called CE quantifiers - one finds the interpretations of determiner phrases in natural languages. The property of monotonicity is also linguistically ubiquitous, though some determiners like an even number of are highly non-monotone. They are nevertheless definable in terms of monotone CE quantifiers: we giv…Read more
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26The Size of a Formula as a Measure of ComplexityIn Åsa Hirvonen, Juha Kontinen, Roman Kossak & Andrés Villaveces (eds.), Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics, De Gruyter. pp. 193-214. 2015.
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On Applications of Transfer Principles in Model TheoryIn Alessandro Andretta (ed.), On Applications of Transfer Principles in Model Theory, Quaderni Di Matematica. 2007.
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32An Ehrenfeucht‐Fraïssé game for Lω1ωMathematical Logic Quarterly 59 (4-5): 357-370. 2013.In this paper we develop an Ehrenfeucht‐Fraïssé game for. Unlike the standard Ehrenfeucht‐Fraïssé games which are modeled solely after the behavior of quantifiers, this new game also takes into account the behavior of connectives in logic. We prove the adequacy theorem for this game. We also apply the new game to prove complexity results about infinite binary strings.
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48The härtig quantifier: A surveyJournal of Symbolic Logic 56 (4): 1153-1183. 1991.A fundamental notion in a large part of mathematics is the notion of equicardinality. The language with Hartig quantifier is, roughly speaking, a first-order language in which the notion of equicardinality is expressible. Thus this language, denoted by LI, is in some sense very natural and has in consequence special interest. Properties of LI are studied in many papers. In [BF, Chapter VI] there is a short survey of some known results about LI. We feel that a more extensive exposition of these r…Read more
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31Trees and Ehrenfeucht–Fraı̈ssé gamesAnnals of Pure and Applied Logic 100 (1-3): 69-97. 1999.Trees are natural generalizations of ordinals and this is especially apparent when one tries to find an uncountable analogue of the concept of the Scott-rank of a countable structure. The purpose of this paper is to introduce new methods in the study of an ordering between trees whose analogue is the usual ordering between ordinals. For example, one of the methods is the tree-analogue of the successor operation on the ordinals
Helsinki, Southern Finland, Finland