On maximum conservative extensions

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Feb 2015Embargo end date: 01 Feb 2013 English Publisher:SAGE PublicationsJournal:Computability, volume 4, pages 57-68 (issn: 2211-3568, eissn: 2211-3576,

Copyright policy )Funded by:NSF | Proof Theoretic Aspects o...

Authors: Henry Towsner;

doi: 10.3233/com-150033 , 10.48550/arxiv.1302.1488

arXiv: 1302.1488

On maximum conservative extensions

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Abstract

We investigate the set of Π 1 2 sentences which are Π 1 1 conservative over theories of second order arithmetic. We exhibit new elements of these sets and conclude that the sets are Π 2 complete. Along the way, we show that, over the theory RCA 0 , induction for Σ n formulas has essentially no consequences for Δ n+1 formulas.

Related Organizations

University of Connecticut
United States
University of Pennsylvania
United States

Keywords

FOS: Mathematics, Mathematics - Logic, Logic (math.LO)

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