Now showing items 1-3 of 3

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      Existentially Closed Models in the Framework of Arithmetic  [Article]

      Adamowicz, Zofia; Cordón Franco, Andrés; Lara Martín, Francisco Félix (The Association for Symbolic Logic, 2016)
      We prove that the standard cut is definable in each existentially closed model of IΔ0 + exp by a (parameter free) П1–formula. This definition is optimal with respect to quantifier complexity and allows us to improve some ...
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      On axiom schemes for T-provably Δ1 formulas  [Article]

      Cordón Franco, Andrés; Fernández Margarit, Alejandro; Lara Martín, Francisco Félix (Springer, 2014)
      This paper investigates the status of the fragments of Peano Arithmetic obtained by restricting induction, collection and least number axiom schemes to formulas which are Δ1 provably in an arithmetic theory T. In ...
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      Some Results on LΔ n+1  [Article]

      Fernández Margarit, Alejandro; Lara Martín, Francisco Félix (Wiley, 2001)
      We study the quantifier complexity and the relative strength of some fragments of arithmetic axiomatized by induction and minimization schemes for Δn+1 formulas.