Journal of Symbolic Logic

A note on Σ1-maximal models

A. Cordón—Franco and F. F. Lara—Martín

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Let T be a recursive theory in the language of first order Arithmetic. We prove that if T extends: (a) the scheme of parameter free Δ1-minimization (plus exp), or (b) the scheme of parameter free Π1-induction, then there are no Σ1-maximal models with respect to T. As a consequence, we obtain a new proof of an unpublished theorem of Jeff Paris stating that Σ1-maximal models with respect to IΔ0 + exp do not satisfy the scheme of Σ1-collection BΣ1.

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J. Symbolic Logic, Volume 72, Issue 3 (2007), 1072-1078.

First available in Project Euclid: 2 October 2007

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Cordón—Franco, A.; Lara—Martín, F. F. A note on Σ 1 -maximal models. J. Symbolic Logic 72 (2007), no. 3, 1072--1078. doi:10.2178/jsl/1191333857.

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