21 found
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  1. Zofia Adamowicz & Teresa Bigorajska (2001). Existentially Closed Structures and Gödel's Second Incompleteness Theorem. Journal of Symbolic Logic 66 (1):349-356.
    We prove that any 1-closed (see def 1.1) model of the Π 2 consequences of PA satisfies ¬Cons PA which gives a proof of the second Godel incompleteness theorem without the use of the Godel diagonal lemma. We prove a few other theorems by the same method.
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  2.  23
    Zofia Adamowicz & Paweł Zbierski (2001). On Herbrand Consistency in Weak Arithmetic. Archive for Mathematical Logic 40 (6):399-413.
    We prove that the Gödel incompleteness theorem holds for a weak arithmetic T = IΔ0 + Ω2 in the form where Cons H (T) is an arithmetic formula expressing the consistency of T with respect to the Herbrand notion of provability.
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  3.  6
    Zofia Adamowicz & Leszek Aleksander Kołodziejczyk (2007). Partial Collapses of the Complexity Hierarchy in Models for Fragments of Bounded Arithmetic. Annals of Pure and Applied Logic 145 (1):91-95.
    For any n, we construct a model of in which each formula is equivalent to an formula.
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  4.  8
    Zofia Adamowicz & Leszek Aleksander Kolodziejczyk (2010). A Note on the E1 Collection Scheme and Fragments of Bounded Arithmetic. Mathematical Logic Quarterly 56 (2):126-130.
    We show that for each n ≥ 1, if T2n does not prove the weak pigeonhole principle for Σbn functions, then the collection scheme B Σ1 is not finitely axiomatizable over T2n. The same result holds with Sn2 in place of T 2n.
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  5.  17
    Zofia Adamowicz (1991). On Maximal Theories. Journal of Symbolic Logic 56 (3):885-890.
  6.  4
    Zofia Adamowicz & Roman Kossak (1988). A Note on BΣn and an Intermediate Induction Schema. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 34 (3):261-264.
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  7.  3
    Zofia Adamowicz (1993). A Contribution to the End-Extension Problem and the Π1 Conservativeness Problem. Annals of Pure and Applied Logic 61 (1-2):3-48.
    We formulate a Π1 sentence τ which is a version of the Tableau consistency of GlΔ0. The sentence τ is true and is provable in GlΔ0 + exp. We construct a model M of GlΔ0+Ω1+τ+BGs1 which has no proper end-extension to a model of GlΔ0+Ω1+τ. Also we prove that GlΔ0+Ω1+τ is not Π1 conservative over GlΔ0+τ.
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  8.  19
    Zofia Adamowicz (1987). Open Induction and the True Theory of Rationals. Journal of Symbolic Logic 52 (3):793-801.
  9.  4
    Zofia Adamowicz (1977). On Finite Lattices of Degrees of Constructibility. Journal of Symbolic Logic 42 (3):349-371.
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  10.  7
    Zofia Adamowicz (1992). A Sharp Version of the Bounded Matijasevich Conjecture and the End- Extension Problem. Journal of Symbolic Logic 57 (2):597-616.
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  11.  14
    Zofia Adamowicz, Leszek Aleksander Kołodziejczyk & Jeff Paris (2012). Truth Definitions Without Exponentiation and the Σ₁ Collection Scheme. Journal of Symbolic Logic 77 (2):649-655.
    We prove that: • if there is a model of I∆₀ + ¬ exp with cofinal Σ₁-definable elements and a Σ₁ truth definition for Σ₁ sentences, then I∆₀ + ¬ exp +¬BΣ₁ is consistent, • there is a model of I∆₀ Ω₁ + ¬ exp with cofinal Σ₁-definable elements, both a Σ₂ and a ∏₂ truth definition for Σ₁ sentences, and for each n > 2, a Σ n truth definition for Σ n sentences. The latter result is obtained by (...)
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  12.  3
    Zofia Adamowicz & Roman Kossak (1988). A Note on BΣn and an Intermediate Induction Schema. Mathematical Logic Quarterly 34 (3):261-264.
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  13.  15
    Zofia Adamowicz & Guillermo Morales-Luna (1985). A Recursive Model for Arithmetic with Weak Induction. Journal of Symbolic Logic 50 (1):49-54.
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  14.  4
    Zofia Adamowicz & Pawe Zbierski (2003). On Complexity Reduction of Σ1 Formulas. Archive for Mathematical Logic 42 (1):45-58.
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  15.  8
    Zofia Adamowicz (1976). On Finite Lattices of Degrees of Constructibility of Reals. Journal of Symbolic Logic 41 (2):313-322.
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  16.  5
    Martın Abadi, Yoshihiro Abe, Francine F. Abeles, Andrew Aberdein, Vicente Aboites, Nathanael Ackerman, Roger D. Acord, Zofia Adamowicz, John W. Addison Jr & Fritz Aeschbach (2003). Individual Members 2003. Bulletin of Symbolic Logic 9 (4).
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  17.  13
    Zofia Adamowicz (1976). One More Aspect of Forcing and Omitting Types. Journal of Symbolic Logic 41 (1):73-80.
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  18.  1
    Zofia Adamowicz, Leszek Aleksander Kolodziejczyk & J. Paris (2012). Truth Definitions Without Exponentiation and the Σ1 Collection Scheme. Journal of Symbolic Logic 77 (2):649.
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  19. Zofia Adamowicz, Andrés Cordón-Franco & F. Félix Lara-martín (2016). Existentially Closed Models in the Framework of Arithmetic. Journal of Symbolic Logic 81 (2):774-788.
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  20. Zofia Adamowicz (1991). On Maximal Theories. Journal of Symbolic Logic 56 (3):885.
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  21. Patrick Farrington, D. S. Scott & Zofia Adamowicz (1989). Hinges and Automorphisms of the Degrees of Non-Constructibility. Journal of Symbolic Logic 54 (3):1109-1111.
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