8 found
  1.  55
    Theories of Arithmetics in Finite Models.Michał Krynicki & Konrad Zdanowski - 2005 - Journal of Symbolic Logic 70 (1):1-28.
    We investigate theories of initial segments of the standard models for arithmetics. It is easy to see that if the ordering relation is definable in the standard model then the decidability results can be transferred from the infinite model into the finite models. On the contrary we show that the Σ₂—theory of multiplication is undecidable in finite models. We show that this result is optimal by proving that the Σ₁—theory of multiplication and order is decidable in finite models as well (...)
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  2.  11
    Hierarchies of Partially Ordered Connectives and Quantifiers.Michał Krynicki - 1993 - Mathematical Logic Quarterly 39 (1):287-294.
    Connections between partially ordered connectives and Henkin quantifiers are considered. It is proved that the logic with all partially ordered connectives and the logic with all Henkin quantifiers coincide. This implies that the hierarchy of partially ordered connectives is strongly hierarchical and gives several nondefinability results between some of them. It is also deduced that each Henkin quantifier can be defined by a quantifier of the form equation imagewhat is a strengthening of the Walkoe result. MSC: 03C80.
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  3.  22
    The Härtig Quantifier: A Survey.Heinrich Herre, Michał Krynicki, Alexandr Pinus & Jouko Väänänen - 1991 - Journal of Symbolic Logic 56 (4):1153-1183.
    A fundamental notion in a large part of mathematics is the notion of equicardinality. The language with Hartig quantifier is, roughly speaking, a first-order language in which the notion of equicardinality is expressible. Thus this language, denoted by LI, is in some sense very natural and has in consequence special interest. Properties of LI are studied in many papers. In [BF, Chapter VI] there is a short survey of some known results about LI. We feel that a more extensive exposition (...)
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  4.  21
    Vector Spaces and Binary Quantifiers.Michał Krynicki, Alistair Lachlan & Jouko Väänänen - 1984 - Notre Dame Journal of Formal Logic 25 (1):72-78.
  5.  18
    On the Semantics of the Henkin Quantifier.Michał Krynicki & Alistair H. Lachlan - 1979 - Journal of Symbolic Logic 44 (2):184-200.
  6.  11
    Decidability Problems in Languages with Henkin Quantifiers.Michał Krynicki & Marcin Mostowski - 1992 - Annals of Pure and Applied Logic 58 (2):149-172.
    Krynicki, M. and M. Mostowski, Decidability problems in languages with Henkin quantifiers, Annals of Pure and Applied Logic 58 149–172.We consider the language L with all Henkin quantifiers Hn defined as follows: Hnx1…xny1…yn φ iff f1…fnx1. ..xn φ, ...,fn). We show that the theory of equality in L is undecidable. The proof of this result goes by interpretation of the word problem for semigroups.Henkin quantifiers are strictly related to the function quantifiers Fn defined as follows: Fnx1…xny1…yn φ iff fx1…xn φ,...,f). (...)
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  7.  14
    Quantifiers Determined by Classes of Binary Relations.Michał Krynicki - 1995 - In M. Krynicki, M. Mostowski & L. Szczerba (eds.), Quantifiers: Logics, Models and Computation. Kluwer Academic Publishers. pp. 125--138.
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  8.  18
    An Axiomatization of the Logic with the Rough Quantifier.Michał Krynicki & Hans-Peter Tuschik - 1991 - Journal of Symbolic Logic 56 (2):608-617.