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MODELS OF POSITIVE TRUTH

Published online by Cambridge University Press:  26 December 2018

MATEUSZ ŁEŁYK  and
BARTOSZ WCISŁO
MATEUSZ ŁEŁYK*
Affiliation:
Institute of Philosophy, University of Warsaw
BARTOSZ WCISŁO*
Affiliation:
Institute of Mathematics, University of Warsaw
*
*INSTITUTE OF PHILOSOPHY UNIVERSITY OF WARSAW WARSAW 00–927, POLAND E-mail: mlelyk@uw.edu.pl
†INSTITUTE OF MATHEMATICS UNIVERSITY OF WARSAW WARSAW 00–927, POLAND E-mail: b.wcislo@mimuw.edu.pl
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Abstract

This paper is a follow-up to [4], in which a mistake in [6] (which spread also to [9]) was corrected. We give a strenghtening of the main result on the semantical nonconservativity of the theory of PT− with internal induction for total formulae ${(\rm{P}}{{\rm{T}}^ - } + {\rm{INT}}\left( {{\rm{tot}}} \right)$, denoted by PT− in [9]). We show that if to PT− the axiom of internal induction for all arithmetical formulae is added (giving ${\rm{P}}{{\rm{T}}^ - } + {\rm{INT}}$), then this theory is semantically stronger than ${\rm{P}}{{\rm{T}}^ - } + {\rm{INT}}\left( {{\rm{tot}}} \right)$. In particular the latter is not relatively truth definable (in the sense of [11]) in the former. Last but not least, we provide an axiomatic theory of truth which meets the requirements put forward by Fischer and Horsten in [9]. The truth theory we define is based on Weak Kleene Logic instead of the Strong one.

Keywords

03H15axiomatic theories of truthconservativitynonstandard models of arithmeticfinite axiomatizabilityspeed-up
Type
Research Article
Information
The Review of Symbolic Logic , Volume 12 , Issue 1 , March 2019 , pp. 144 - 172
Copyright
Copyright © Association for Symbolic Logic 2018 

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