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DISJUNCTIONS WITH STOPPING CONDITIONS

Part of: Proof theory and constructive mathematics Philosophical aspects of logic and foundations Nonstandard models

Published online by Cambridge University Press:  05 January 2021

ROMAN KOSSAK  and
BARTOSZ WCISŁO
ROMAN KOSSAK
Affiliation:
THE GRADUATE CENTER CITY UNIVERSITY OF NEW YORK 365 FIFTH AVENUE, NEW YORK, NY 10016, USA E-mail: RKossak@gc.cuny.edu
BARTOSZ WCISŁO
Affiliation:
INSTITUTE OF MATHEMATICS POLISH ACADEMY OF SCIENCES UL. ŚNIADECKICH 800-656 WARSAW, POLAND E-mail: bar.wcislo@gmail.com
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Abstract

We introduce a tool for analysing models of $\text {CT}^-$, the compositional truth theory over Peano Arithmetic. We present a new proof of Lachlan’s theorem that the arithmetical part of models of $\text {CT}^-$ are recursively saturated. We also use this tool to provide a new proof of theorem from [8] that all models of $\text {CT}^-$ carry a partial inductive truth predicate. Finally, we construct a partial truth predicate defined for a set of formulae whose syntactic depth forms a nonstandard cut which cannot be extended to a full truth predicate satisfying $\text {CT}^-$.

Keywords

truth theoriestruth predicatessatisfaction classesPeano Arithmeticmodels of arithmeticrecursive saturation

MSC classification

Primary: 03H15: Nonstandard models of arithmetic
Secondary: 03F30: First-order arithmetic and fragments 03A99: None of the above, but in this section

Information

Type
Articles
Information
Bulletin of Symbolic Logic , Volume 27 , Issue 3 , September 2021 , pp. 231 - 253
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Copyright
© 2021, Association for Symbolic Logic

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