Mathematical Logic Quarterly 51 (3):313-328 (2005)

Andrés Cordón
Universidad de Sevilla
Felicity Martin
University of Sydney
By a theorem of R. Kaye, J. Paris and C. Dimitracopoulos, the class of the Πn+1-sentences true in the standard model is the only consistent Πn+1-theory which extends the scheme of induction for parameter free Πn+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, finite axiomatizability and relative strength of schemes for Δn+1-formulas
Keywords quantifier complexity  Fragments of Arithmetic  parameter free schemes  Δn+1‐formulas  true sentences
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DOI 10.1002/malq.200410034
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References found in this work BETA

On the Scheme of Induction for Bounded Arithmetic Formulas.A. J. Wilkie & J. B. Paris - 1987 - Annals of Pure and Applied Logic 35 (3):261-302.
On the Induction Schema for Decidable Predicates.Lev D. Beklemishev - 2003 - Journal of Symbolic Logic 68 (1):17-34.

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Citations of this work BETA

A Note On Σ1-Maximal Models.A. Cordón—Franco & F. F. Lara—Martín - 2007 - Journal of Symbolic Logic 72 (3):1072-1078.

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