4 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.  5
    Strongly Maximal Subgroups Determined by Elements in Interstices.Teresa Bigorajska - 2003 - Mathematical Logic Quarterly 49 (1):101-108.
    Continuing the earlier research in [1] and [4] we work out a class of interstices in countable arithmetically saturated models of PA in which selective types are realized and a class of interstices in which 2-indiscernible types are realized.
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  3.  6
    Universal Induction and True Universal Arithmetic.Teresa Bigorajska - 1994 - Mathematical Logic Quarterly 40 (1):103-105.
    We prove that every finitely generated model for induction for universal formulas without parameters satisfies also all true universal sentences.
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  4.  18
    On Σ1‐Definable Functions Provably Total in I ∏ 1−.Teresa Bigorajska - 1995 - Mathematical Logic Quarterly 41 (1):135-137.
    We prove the following theorem: Let φ be a formula in the language of the theory PA− of discretely ordered commutative rings with unit of the form ∃yφ′ with φ′ and let ∈ Δ0 and let fφ: ℕ → ℕ such that fφ = y iff φ′ & < xK). Here I ∏math image1− denotes the theory PA− plus the scheme of induction for formulas φ of the form ∀yφ′ with φ′ ∈ Δ0.
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