A contribution to the end-extension problem and the Π1 conservativeness problem

Annals of Pure and Applied Logic 61 (1-2):3-48 (1993)
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Abstract

We formulate a Π1 sentence τ which is a version of the Tableau consistency of GlΔ0. The sentence τ is true and is provable in GlΔ0 + exp. We construct a model M of GlΔ0+Ω1+τ+BGs1 which has no proper end-extension to a model of GlΔ0+Ω1+τ. Also we prove that GlΔ0+Ω1+τ is not Π1 conservative over GlΔ0+τ

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10.1016/0168-0072(93)90196-k

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Citations of this work

A small reflection principle for bounded arithmetic.Rineke Verbrugge & Albert Visser - 1994 - Journal of Symbolic Logic 59 (3):785-812.
End extensions of models of fragments of PA.C. Dimitracopoulos & V. Paschalis - 2020 - Archive for Mathematical Logic 59 (7-8):817-833.

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References found in this work

On the scheme of induction for bounded arithmetic formulas.A. J. Wilkie & J. B. Paris - 1987 - Annals of Pure and Applied Logic 35 (C):261-302.
On maximal theories.Zofia Adamowicz - 1991 - Journal of Symbolic Logic 56 (3):885-890.
On Maximal Theories.Zofia Adamowicz - 1991 - Journal of Symbolic Logic 56 (3):885-890.
A Note on BΣn and an Intermediate Induction Schema.Zofia Adamowicz & Roman Kossak - 1988 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 34 (3):261-264.

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