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  1.  17
    Models of Intuitionistic TT and N.Daniel Dzierzgowski - 1995 - Journal of Symbolic Logic 60 (2):640-653.
    Let us define the intuitionistic part of a classical theory T as the intuitionistic theory whose proper axioms are identical with the proper axioms of T. For example, Heyting arithmetic HA is the intuitionistic part of classical Peano arithmetic PA. It's a well-known fact, proved by Heyting and Myhill, that ZF is identical with its intuitionistic part. In this paper, we mainly prove that TT, Russell's Simple Theory of Types, and NF, Quine's "New Foundations," are not equal to their intuitionistic (...)
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  2.  26
    Typical Ambiguity and Elementary Equivalence.Daniel Dzierzgowski - 1993 - Mathematical Logic Quarterly 39 (1):436-446.
    A sentence of the usual language of set theory is said to be stratified if it is obtained by “erasing” type indices in a sentence of the language of Russell's Simple Theory of Types. In this paper we give an alternative presentation of a proof the ambiguity theorem stating that any provable stratified sentence has a stratified proof. To this end, we introduce a new set of ambiguity axioms, inspired by Fraïssé's characterization of elementary equivalence; these axioms can be naturally (...)
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  3.  12
    Intuitionistic Typical Ambiguity.Daniel Dzierzgowski - 1992 - Archive for Mathematical Logic 31 (3):171-182.
  4.  12
    Constants in Kripke Models for Intuitionistic Logic.Daniel Dzierzgowski - 1995 - Mathematical Logic Quarterly 41 (4):431-441.
    We present a technique to extend a Kripke structure into an elementary extension satisfying some property which can be “axiomatized” by a family of sets of sentences, where, most often, many constant symbols occur. To that end, we prove extended theorems of completeness and compactness. Also, a section of the paper is devoted to the back-and-forth construction of isomorphisms between Kripke structures.
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  5.  18
    Finite Sets and Natural Numbers in Intuitionistic TT Without Extensionality.Daniel Dzierzgowski - 1998 - Studia Logica 61 (3):417-428.
    In this paper, we prove that Heyting's arithmetic can be interpreted in an intuitionistic version of Russell's Simple Theory of Types without extensionality.
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  6. A Note on Frai'sse's Characterization of Elementary Equivalence.Daniel Dzierzgowski - 1990 - Logique Et Analyse 131 (132):273-286.
  7.  10
    Finite Sets and Natural Numbers in Intuitionistic TT.Daniel Dzierzgowski - 1996 - Notre Dame Journal of Formal Logic 37 (4):585-601.
    We show how to interpret Heyting's arithmetic in an intuitionistic version of TT, Russell's Simple Theory of Types. We also exhibit properties of finite sets in this theory and compare them with the corresponding properties in classical TT. Finally, we prove that arithmetic can be interpreted in intuitionistic TT, the subsystem of intuitionistic TT involving only three types. The definitions of intuitionistic TT and its finite sets and natural numbers are obtained in a straightforward way from the classical definitions. This (...)
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  8.  5
    Many-Sorted Elementary Equivalence.Daniel Dzierzgowski - 1988 - Notre Dame Journal of Formal Logic 29 (4):530-542.