Reflection using the derivability conditions

Sean Matthews, Alex Simpson

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The authors consider a recursively axiomatized arithmetic T with a new primitive predicate Pr characterized by axioms (C1)–(C3) based on Löb’s derivability conditions (denote this new theory by T ' ). It is shown that T ' +R, where R is the reflection scheme, is conservative over T. It is also proved that the theory IΣ 1 ' +R contains Peano arithmetic PA where IΣ 1 ' is arithmetic with induction for Σ 1 formulas in the language with Pr and axioms (C1)–(C3) as well as that PA ' +R is a conservative extension of PA.
Original languageEnglish
Title of host publicationProceedings of the international conference dedicated to the memory of Roberto Magari, April 26–30, 1994, Pontignano, Italy.
EditorsAldo Ursini, Paolo Agliano
Place of PublicationNew York
PublisherMARCEL DEKKER
Pages603 - 616
Number of pages14
ISBN (Print)9780824796068
Publication statusPublished - 30 May 1996

Publication series

NameLecture Notes Pure Applied Mathematics
PublisherMarcel Dekker Inc
Volume180

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