
25Logicality and model classesBulletin of Symbolic Logic 27 (4): 385414. 2021.We ask, when is a property of a model a logical property? According to the socalled Tarski–Sher criterion this is the case when the property is preserved by isomorphisms. We relate this to modeltheoretic 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

28Inner models from extended logics: Part 1Journal of Mathematical Logic 21 (2): 2150012. 2020.If we replace firstorder logic by secondorder logic in the original definition of Gödel’s inner model L, we obtain the inner model of hereditarily ordinal definable sets [33]. In this paper...

17When cardinals determine the power set: inner models and Härtig quantifier logicMathematical Logic Quarterly. forthcoming.We show that the predicate “x is the power set of y” is ‐definable, if V = L[E] is an extender model constructed from a coherent sequences of extenders, provided that there is no inner model with a Woodin cardinal. Here is a predicate true of just the infinite cardinals. From this we conclude: the validities of second order logic are reducible to, the set of validities of the Härtig quantifier logic. Further we show that if no L[E] model has a cardinal strong up to one of its ℵ‐fixed points, and…Read more

8The Strategic Balance of Games in LogicIn Alessandra Palmigiano & Mehrnoosh Sadrzadeh (eds.), Samson Abramsky on Logic and Structure in Computer Science and Beyond, Springer Verlag. pp. 755770. 2023.Truth, consistency and elementary equivalence can all be characterised in terms of games, namely the socalled evaluation game, the modelexistence game, and the Ehrenfeucht–Fraisse game. We point out the great affinity of these games to each other and call this phenomenon the strategic balance in logic. In particular, we give explicit translations of strategies from one game to another.

8An atom’s worth of anonymityLogic Journal of the IGPL 31 (6): 10781083. 2023.I contribute this paper on anonymity to honor the birthday of John Crossley. I am not only John’s friend, but also his grandson in the academic sense—as my doct.

18Positive logicsArchive for Mathematical Logic 62 (1): 207223. 2023.Lindström’s Theorem characterizes first order logic as the maximal logic satisfying the Compactness Theorem and the Downward LöwenheimSkolem 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 LöwenheimSko…Read more

35Tracing Internal CategoricityTheoria 87 (4): 9861000. 2020.Theoria, Volume 87, Issue 4, Page 9861000, August 2021.

19An Overview of Saharon Shelah's Contributions to Mathematical Logic, in Particular to Model TheoryTheoria 87 (2): 349360. 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.

2023rd Workshop on Logic, Language, Information and Computation  WoLLIC 2016Annals of Pure and Applied Logic 170 (9): 921922. 2019.

24K. Jon Barwise. Absolute logics and. Annals of mathematical logic, vol. 4 no. 3 , pp. 309–340Journal of Symbolic Logic 50 (1): 240241. 1985.

21J. 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): 241242. 1985.

30A logical approach to contextspecific independenceAnnals of Pure and Applied Logic 170 (9): 975992. 2019.Directed acyclic graphs (DAGs) constitute a qualitative representation for conditional independence (CI) properties of a probability distribution. It is known that every CI statement implied by the topology of a DAG is witnessed over it under a graphtheoretic criterion of dseparation. Alternatively, all such implied CI statements are derivable from the local independencies encoded by a DAG using the socalled semigraphoid axioms. We consider Labeled Directed Acyclic Graphs (LDAGs) modeling gr…Read more

34An extension of a theorem of zermeloBulletin of Symbolic Logic 25 (2): 208212. 2019.We show that if $$ satisfies the firstorder Zermelo–Fraenkel axioms of set theory when the membership relation is ${ \in _1}$ and also when the membership relation is ${ \in _2}$, and in both cases the formulas are allowed to contain both ${ \in _1}$ and ${ \in _2}$, then $\left \cong \left$, and the isomorphism is definable in $$. This extends Zermelo’s 1930 theorem in [6].

The Logic of Approximate DependenceIn Ramaswamy Ramanujam, Lawrence Moss & Can Başkent (eds.), Rohit Parikh on Logic, Language and Society, Springer Verlag. 2017.

European Summer School in Logic, Language and Information: ESSLLI 1997: Generalized Quantifiers and Computation (edited book)Springer. 1999.

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2523rd Workshop on Logic, Language, Information and ComputationLogic Journal of the IGPL 25 (2): 253272. 2017.

31A logic for arguing about probabilities in measure teamsArchive for Mathematical Logic 56 (56): 475489. 2017.We use sets of assignments, a.k.a. teams, and measures on them to define probabilities of firstorder formulas in given data. We then axiomatise firstorder 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.

36Decidability of Some Logics with Free Quantifier VariablesMathematical Logic Quarterly 27 (26): 1722. 1981.

45Generalized quantifiers and pebble games on finite structuresAnnals of Pure and Applied Logic 74 (1): 2375. 1995.Firstorder logic is known to have a severely limited expressive power on finite structures. As a result, several different extensions have been investigated, including fragments of secondorder logic, fixpoint logic, and the infinitary logic L∞ωω in which every formula has only a finite number of variables. In this paper, we study generalized quantifiers in the realm of finite structures and combine them with the infinitary logic L∞ωω to obtain the logics L∞ωω, where Q = {Qi: iε I} is a family …Read more

66Dependence logic: a new approach to independence friendly logicCambridge University Press. 2007.Dependence is a common phenomenon, wherever one looks: ecological systems, astronomy, human history, stock markets  but what is the logic of dependence? This book is the first to carry out a systematic logical study of this important concept, giving on the way a precise mathematical treatment of Hintikka’s independence friendly logic. Dependence logic adds the concept of dependence to first order logic. Here the syntax and semantics of dependence logic are studied, dependence logic is given an …Read more

167Secondorder logic and foundations of mathematicsBulletin of Symbolic Logic 7 (4): 504520. 2001.We discuss the differences between firstorder set theory and secondorder logic as a foundation for mathematics. We analyse these languages in terms of two levels of formalization. The analysis shows that if secondorder logic is understood in its full semantics capable of characterizing categorically central mathematical concepts, it relies entirely on informal reasoning. On the other hand, if it is given a weak semantics, it loses its power in expressing concepts categorically. Firstorder se…Read more
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