20 found
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  1. Existentially Closed Structures and Gödel's Second Incompleteness Theorem.Zofia Adamowicz & Teresa Bigorajska - 2001 - 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.  13
    Existentially Closed Models in the Framework of Arithmetic.Zofia Adamowicz, Andrés Cordón-Franco & F. Félix Lara-martín - 2016 - Journal of Symbolic Logic 81 (2):774-788.
  3.  38
    On Herbrand Consistency in Weak Arithmetic.Zofia Adamowicz & Paweł Zbierski - 2001 - 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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  4.  33
    Truth Definitions Without Exponentiation and the Σ₁ Collection Scheme.Zofia Adamowicz, Leszek Aleksander Kołodziejczyk & Jeff Paris - 2012 - 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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  5.  14
    On Maximal Theories.Zofia Adamowicz - 1991 - Journal of Symbolic Logic 56 (3):885-890.
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  6.  31
    On Maximal Theories.Zofia Adamowicz - 1991 - Journal of Symbolic Logic 56 (3):885-890.
  7.  29
    A Sharp Version of the Bounded Matijasevich Conjecture and the End- Extension Problem.Zofia Adamowicz - 1992 - Journal of Symbolic Logic 57 (2):597-616.
  8.  41
    A Note on BΣn and an Intermediate Induction Schema.Zofia Adamowicz & Roman Kossak - 1988 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 34 (3):261-264.
  9.  6
    Truth Definitions Without Exponentiation and the Σ1 Collection Scheme.Zofia Adamowicz, Leszek Aleksander Kolodziejczyk & J. Paris - 2012 - Journal of Symbolic Logic 77 (2):649.
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  10.  10
    A Contribution to the End-Extension Problem and the Π1 Conservativeness Problem.Zofia Adamowicz - 1993 - 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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  11.  20
    Partial Collapses of the Complexity Hierarchy in Models for Fragments of Bounded Arithmetic.Zofia Adamowicz & Leszek Aleksander Kołodziejczyk - 2007 - 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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  12.  51
    Open Induction and the True Theory of Rationals.Zofia Adamowicz - 1987 - Journal of Symbolic Logic 52 (3):793-801.
  13.  37
    On Finite Lattices of Degrees of Constructibility.Zofia Adamowicz - 1977 - Journal of Symbolic Logic 42 (3):349-371.
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  14.  33
    A Note on the E1 Collection Scheme and Fragments of Bounded Arithmetic.Zofia Adamowicz & Leszek Aleksander Kołodziejczyk - 2010 - 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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  15.  30
    On Finite Lattices of Degrees of Constructibility of Reals.Zofia Adamowicz - 1976 - Journal of Symbolic Logic 41 (2):313-322.
  16.  25
    Individual Members 2003.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 - Bulletin of Symbolic Logic 9 (4).
  17.  31
    A Recursive Model for Arithmetic with Weak Induction.Zofia Adamowicz & Guillermo Morales-Luna - 1985 - Journal of Symbolic Logic 50 (1):49-54.
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  18.  30
    One More Aspect of Forcing and Omitting Types.Zofia Adamowicz - 1976 - Journal of Symbolic Logic 41 (1):73-80.
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  19.  7
    On Complexity Reduction of Σ1 Formulas.Zofia Adamowicz & Pawe Zbierski - 2003 - Archive for Mathematical Logic 42 (1):45-58.
    . For a fixed q  ℕ and a given Σ1 definition φ, where d is a parameter, we construct a model M of 1 Δ0 + ¬ exp and a non standard d  M such that in M either φ has no witness smaller than d or phgr; is equivalent to a formula ϕ having no more than q alternations of blocks of quantifiers.
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  20.  6
    Hinges and Automorphisms of the Degrees of Non-Constructibility.Patrick Farrington, D. S. Scott & Zofia Adamowicz - 1989 - Journal of Symbolic Logic 54 (3):1109-1111.