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DISJUNCTIONS WITH STOPPING CONDITIONS

Published online by Cambridge University Press:  05 January 2021

ROMAN KOSSAK
Affiliation:
THE GRADUATE CENTER CITY UNIVERSITY OF NEW YORK 365 FIFTH AVENUE, NEW YORK, NY10016, USAE-mail: RKossak@gc.cuny.edu
BARTOSZ WCISŁO
Affiliation:
INSTITUTE OF MATHEMATICS POLISH ACADEMY OF SCIENCES UL. ŚNIADECKICH 800-656WARSAW, POLANDE-mail: bar.wcislo@gmail.com

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 $\text {CT}^-$ .

Type
Articles
Copyright
© 2021, Association for Symbolic Logic

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