4 found
Sort by:
  1.  56 DLs
    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.
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  2.  2 DLs
    Teresa Bigorajska (1994). Universal Induction and True Universal Arithmetic. 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.
    No categories
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  3.  2 DLs
    Teresa Bigorajska (1995). On Σ1‐Definable Functions Provably Total in I ∏ 1−. 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.
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  4.  0 DLs
    Teresa Bigorajska (2003). Strongly Maximal Subgroups Determined by Elements in Interstices. 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.
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation