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Fragments of Arithmetic and true sentences


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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: 2005
Published in: Mathematical Logic Quaterly, 51 (3), 313-328.
Document type: Article
Abstract: By a theorem of R. Kaye, J. Paris and C. Dimitracopoulos, the class of the ¦n+1–sentences true in the standard model is the only (up to deductive equivalence) consistent ¦n+1–theory which extends the scheme of induction for parameter free ¦n+1–formulas. Motivated by this result, we present a systematic study of extensions of bounded quantifier complexity of fragments of first–order Peano Arithmetic. Here, we improve that result and show that this property describes a general phenomenon valid for parameter free schemes. As a consequence, we obtain results on the quantifier complexity, (non)finite axiomatizability and relative strength of schemes for ¢n+1–formulas.
Cite: Cordón Franco, A., Fernández Margarit, A. y Lara Martín, F.F. (2005). Fragments of Arithmetic and true sentences. Mathematical Logic Quaterly, 51 (3), 313-328.
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DOI: 10.1002/malq.200410034

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