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  1.  30
    On Intermediate Predicate Logics of Some Finite Kripke Frames, I. Levelwise Uniform Trees.Dmitrij Skvortsov - 2004 - Studia Logica 77 (3):295 - 323.
    An intermediate predicate logic L is called finite iff it is characterized by a finite partially ordered set M, i.e., iff L is the logic of the class of all predicate Kripke frames based on M. In this paper we study axiomatizability of logics of this kind. Namely, we consider logics characterized by finite trees M of a certain type (levelwise uniform trees) and establish the finite axiomatizability criterion for this case.
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  2.  37
    On the Predicate Logic of Linear Kripke Frames and Some of its Extensions.Dmitrij Skvortsov - 2005 - Studia Logica 81 (2):261-282.
    We propose a new, rather simple and short proof of Kripke-completeness for the predicate variant of Dummett's logic. Also a family of Kripke-incomplete extensions of this logic that are complete w.r.t. Kripke frames with equality (or equivalently, w.r.t. Kripke sheaves [8]), is described.
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  3.  33
    Kripke Sheaf Completeness of Some Superintuitionistic Predicate Logics with a Weakened Constant Domains Principle.Dmitrij Skvortsov - 2012 - Studia Logica 100 (1-2):361-383.
    The completeness w.r.t. Kripke frames with equality (or, equivalently, w.r.t. Kripke sheaves, [ 8 ] or [4, Sect. 3.6]) is established for three superintuitionistic predicate logics: ( Q - H + D *), ( Q - H + D *&K), ( Q - H + D *& K & J ). Here Q - H is intuitionistic predicate logic, J is the principle of the weak excluded middle, K is Kuroda’s axiom, and D * (cf. [ 12 ]) is a (...)
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  4.  23
    On Some Kripke Complete and Kripke Incomplete Intermediate Predicate Logics.Dmitrij Skvortsov - 1998 - Studia Logica 61 (2):281-292.
    The Kripke-completeness and incompleteness of some intermediate predicate logics is established. In particular, we obtain a Kripke-incomplete logic (H* +A+D+K) where H* is the intuitionistic predicate calculus, A is a disjunction-free propositional formula, D = x(P(x) V Q) xP(x) V Q, K = ¬¬x(P(x) V ¬P(x)) (the negative answer to a question of T. Shimura).
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  5.  27
    The Superintuitionistic Predicate Logic of Finite Kripke Frames Is Not Recursively Axiomatizable.Dmitrij Skvortsov - 2005 - Journal of Symbolic Logic 70 (2):451 - 459.
    We prove that an intermediate predicate logic characterized by a class of finite partially ordered sets is recursively axiomatizable iff it is "finite", i.e., iff it is characterized by a single finite partially ordered set. Therefore, the predicate logic LFin of the class of all predicate Kripke frames with finitely many possible worlds is not recursively axiomatizable.
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  6.  21
    Not Every "Tabular" Predicate Logic is Finitely Axiomatizable.Dmitrij Skvortsov - 1997 - Studia Logica 59 (3):387-396.
    An example of finite tree Mo is presented such that its predicate logic (i.e. the intermediate predicate logic characterized by the class of all predicate Kripke frames based on Mo) is not finitely axiomatizable. Hence it is shown that the predicate analogue of de Jongh - McKay - Hosoi's theorem on the finite axiomatizability of every finite intermediate propositional logic is not true.
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  7.  1
    A Remark on Propositional Kripke Frames Sound for Intuitionistic Logic.Dmitrij Skvortsov - 2010 - In Lev Beklemishev, Valentin Goranko & Valentin Shehtman (eds.), Advances in Modal Logic, Volume 8. CSLI Publications. pp. 392-410.
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  8.  1
    A Remark on Peculiarity in the Functor Semantic for Superintuitionistic Predicate Logics with Equality.Dmitrij Skvortsov - 2012 - In Thomas Bolander, Torben Braüner, Silvio Ghilardi & Lawrence Moss (eds.), Advances in Modal Logic, Volume 9. CSLI Publications. pp. 483-493.
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