A note on Σ1-maximal models
A. Cordón—Franco and F. F. Lara—Martín
Source: J. Symbolic Logic Volume 72, Issue 3
(2007), 1072-1078.
Abstract
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free Π1-induction, then there are no Σ1-maximal models with respect to T. As a consequence, we obtain a new proof of an unpublished theorem of Jeff Paris stating that Σ1-maximal models with respect to IΔ0 + exp do not satisfy the scheme of Σ1-collection BΣ1.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1191333857
Digital Object Identifier: doi:10.2178/jsl/1191333857
Mathematical Reviews number (MathSciNet): MR2354916
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