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Marek Zawadowski [8]Marek W. Zawadowski [3]
  1. Silvio Ghilardi & Marek Zawadowski (1997). Model Completions and R-Heyting Categories. Annals of Pure and Applied Logic 88 (1):27-46.
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  2. Silvio Ghilardi & Marek Zawadowski (1995). A Sheaf Representation and Duality for Finitely Presented Heyting Algebras. Journal of Symbolic Logic 60 (3):911-939.
    A. M. Pitts in [Pi] proved that HA op fp is a bi-Heyting category satisfying the Lawrence condition. We show that the embedding $\Phi: HA^\mathrm{op}_\mathrm{fp} \longrightarrow Sh(\mathbf{P_0,J_0})$ into the topos of sheaves, (P 0 is the category of finite rooted posets and open maps, J 0 the canonical topology on P 0 ) given by $H \longmapsto HA(H,\mathscr{D}(-)): \mathbf{P_0} \longrightarrow \text{Set}$ preserves the structure mentioned above, finite coproducts, and subobject classifier, it is also conservative. This whole structure on HA op (...)
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  3. Silvio Ghilardi & Marek Zawadowski (1995). Undefinability of Propositional Quantifiers in the Modal System S. Studia Logica 55 (2):259 - 271.
    We show that (contrary to the parallel case of intuitionistic logic, see [7], [4]) there does not exist a translation fromS42 (the propositional modal systemS4 enriched with propositional quantifiers) intoS4 that preserves provability and reduces to identity for Boolean connectives and.
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  4. Marek Zawadowski (1995). Pitts Andrew M.. Interpolation and Conceptual Completeness for Pretoposes Via Category Theory. Mathematical Logic and Theoretical Computer Science, Edited by David W. Kueker, Edgar GK Lopez-Escobar and Carl H. Smith, Lecture Notes in Pure and Applied Mathematics, Vol. 106, Marcel Dekker, New York and Basel 1987, Pp. 301–327. Pitts Andrew M.. Conceptual Completeness for First-Order Intuitionistic Logic: An Application of Categorical Logic. Annals of Pure and Applied Logic, Vol. 41 (1989), Pp. 33–81. [REVIEW] Journal of Symbolic Logic 60 (2):692-694.
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  5. Marek Zawadowski (1995). Review: Andrew M. Pitts, David W. Kueker, Edgar G. K. Lopez-Escobar, Carl H. Smith, Interpolation and Conceptual Completeness for Pretoposes Via Category Theory; Andrew M. Pitts, Conceptual Completeness for First-Order Intutionistic Logic: An Application of Categorical Logic. [REVIEW] Journal of Symbolic Logic 60 (2):692-694.
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  6. Marek W. Zawadowski (1995). Descent and Duality. Annals of Pure and Applied Logic 71 (2):131-188.
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  7. Marek W. Zawadowski (1995). Pre-Ordered Quantifiers in Elementary Sentences of Natural Language. In. In M. Krynicki, M. Mostowski & L. Szczerba (eds.), Quantifiers: Logics, Models and Computation. Kluwer Academic Publishers. 237--253.
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  8. Gonzalo E. Reyes & Marek W. Zawadowski (1993). Formal Systems for Modal Operators on Locales. Studia Logica 52 (4):595 - 613.
    In the paper [8], the first author developped a topos- theoretic approach to reference and modality. (See also [5]). This approach leads naturally to modal operators on locales (or spaces without points). The aim of this paper is to develop the theory of such modal operators in the context of the theory of locales, to axiomatize the propositional modal logics arising in this context and to study completeness and decidability of the resulting systems.
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  9. Andrzej W. Jankowski & Marek Zawadowski (1985). Sheaves Over Heyting Lattices. Studia Logica 44 (3):237 - 256.
    For a complete Heyting lattice , we define a category Etale (). We show that the category Etale () is equivalent to the category of the sheaves over , Sh(), hence also with -valued sets, see [2], [1]. The category Etale() is a generalization of the category Etale (X), see [1], where X is a topological space.
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  10. Marek Zawadowski (1985). The Skolem-Löwenheim Theorem in Toposes. II. Studia Logica 44 (1):25 - 38.
    This paper is a continuation of the investigation from [13]. The main theorem states that the general and the existential quantifiers are (, -reducible in some Grothendieck toposes. Using this result and Theorems 4.1, 4.2 [13] we get the downward Skolem-Löwenheim theorem for semantics in these toposes.
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  11. Marek Zawadowski (1983). The Skolem-Löwenheim Theorem in Toposes. Studia Logica 42 (4):461 - 475.
    The topos theory gives tools for unified proofs of theorems for model theory for various semantics and logics. We introduce the notion of power and the notion of generalized quantifier in topos and we formulate sufficient condition for such quantifiers in order that they fulfil downward Skolem-Löwenheim theorem when added to the language. In the next paper, in print, we will show that this sufficient condition is fulfilled in a vast class of Grothendieck toposes for the general and the existential (...)
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