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Alex Citkin [3]Alexander Citkin [2]
  1. Alex Citkin (2013). Characteristic Formulas of Partial Heyting Algebras. Logica Universalis 7 (2):167-193.
    The goal of this paper is to generalize a notion of characteristic (or Jankov) formula by using finite partial Heyting algebras instead of the finite subdirectly irreducible algebras: with every finite partial Heyting algebra we associate a characteristic formula, and we study the properties of these formulas. We prove that any intermediate logic can be axiomatized by such formulas. We further discuss the correlations between characteristic formulas of finite partial algebras and canonical formulas. Then with every well-connected Heyting algebra we (...)
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  2. Alex Citkin (2012). Not Every Splitting Heyting or Interior Algebra is Finitely Presentable. Studia Logica 100 (1-2):115-135.
    We give an example of a variety of Heyting algebras and of a splitting algebra in this variety that is not finitely presentable. Moreover, we show that the corresponding splitting pair cannot be defined by any finitely presentable algebra. Also, using the Gödel-McKinsey-Tarski translation and the Blok-Esakia theorem, we construct a variety of Grzegorczyk algebras with similar properties.
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  3. Alexander Citkin (2012). A Note on Admissible Rules and the Disjunction Property in Intermediate Logics. Archive for Mathematical Logic 51 (1-2):1-14.
    With any structural inference rule A/B, we associate the rule ${(A \lor p)/(B \lor p)}$ , providing that formulas A and B do not contain the variable p. We call the latter rule a join-extension ( ${\lor}$ -extension, for short) of the former. Obviously, for any intermediate logic with disjunction property, a ${\lor}$ -extension of any admissible rule is also admissible in this logic. We investigate intermediate logics, in which the ${\lor}$ -extension of each admissible rule is admissible. We prove (...)
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  4. Alex Citkin (2010). Metalogic of Intuitionistic Propositional Calculus. Notre Dame Journal of Formal Logic 51 (4):485-502.
    With each superintuitionistic propositional logic L with a disjunction property we associate a set of modal logics the assertoric fragment of which is L . Each formula of these modal logics is interdeducible with a formula representing a set of rules admissible in L . The smallest of these logics contains only formulas representing derivable in L rules while the greatest one contains formulas corresponding to all admissible in L rules. The algebraic semantic for these logics is described.
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  5. Alexander Citkin (2008). A Mind of a Non-Countable Set of Ideas. Logic and Logical Philosophy 17 (1-2):23-39.
    The paper is dedicated to the 80th birthday of the outstanding Russian logician A.V. Kuznetsov. It is addressing a history of the ideas and research conducted by him in non-classical and intermediate logics.
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