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Fragments of Arithmetic and true sentences

✍ Scribed by Andrés Cordón-Franco; Alejandro Fernández-Margarit; F. Félix Lara-Martín

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
246 KB
Volume
51
Category
Article
ISSN
0044-3050

No coin nor oath required. For personal study only.

✦ Synopsis

Paris and C. Dimitracopoulos, the class of the Πn+1-sentences true in the standard model is the only (up to deductive equivalence) 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, (non)finite axiomatizability and relative strength of schemes for ∆n+1-formulas.

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