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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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7When 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
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5The 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. 755-770. 2023.Truth, consistency and elementary equivalence can all be characterised in terms of games, namely the so-called evaluation game, the model-existence 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.
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2An atom’s worth of anonymityLogic Journal of the IGPL 31 (6): 1078-1083. 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.
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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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European Summer School in Logic, Language and Information: ESSLLI 1997: Generalized Quantifiers and Computation (edited book)Springer. 1999.
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Craig's theorem and syntax of abstract logicsBulletin of the Section of Logic 11 (1-2): 82-83. 1982.The Craig Interpolation Theorem is a fundamental property of rst order logic L!!. What happens if we strengthen rst order logic? Second order logic L 2 satises Craig for trivial reasons but on the other hand, L 2 is not very interesting from a fundational point of view
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On the Number of Automorphisms of Uncountable ModelsJournal of Symbolic Logic 59 (4): 1402-1418. 1994.Let $\sigma$ denote the number of automorphisms of a model $\mathfrak{U}$ of power $\omega_1$. We derive a necessary and sufficient condition in terms of trees for the existence of an $\mathfrak{U}$ with $\omega_1 < \sigma < 2^{\omega_1}$. We study the sufficiency of some conditions for $\sigma = 2^{\omega_1}$. These conditions are analogous to conditions studied by D. Kueker in connection with countable models.
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The Logic of Approximate DependenceIn Ramaswamy Ramanujam, Lawrence Moss & Can Başkent (eds.), Rohit Parikh on Logic, Language and Society, Springer Verlag. 2017.
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