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MODELS OF POSITIVE TRUTH

  • MATEUSZ ŁEŁYK (a1) and BARTOSZ WCISŁO (a2)
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.

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Corresponding author
*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
References
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The Review of Symbolic Logic
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