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On axiom schemes for T-provably Δ1 formulas

 

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Author: Cordón Franco, Andrés
Fernández Margarit, Alejandro
Lara Martín, Francisco Félix
Department: Universidad de Sevilla. Departamento de Ciencias de la Computación e Inteligencia Artificial
Date: 2014
Published in: Archive for Mathematical Logic, 53 (3-4), 327-349.
Document type: Article
Abstract: 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 particular, we determine the provably total computable functions of this kind of theories. As an application, we obtain a reduction of the problem whether IΔ0+¬exp implies BΣ1 to a purely recursion-theoretic question.
Cite: Cordón Franco, A., Fernández Margarit, A. y Lara Martín, F.F. (2014). On axiom schemes for T-provably Δ1 formulas. Archive for Mathematical Logic, 53 (3-4), 327-349.
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URI: https://hdl.handle.net/11441/87552

DOI: 10.1007/s00153-014-0368-9

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