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MODELS OF PT– WITH INTERNAL INDUCTION FOR TOTAL FORMULAE

Published online by Cambridge University Press:  15 December 2016

CEZARY CIEŚLIŃSKI ,
MATEUSZ ŁEŁYK  and
BARTOSZ WCISŁO
CEZARY CIEŚLIŃSKI*
Affiliation:
Institute of Philosophy, University of Warsaw
MATEUSZ ŁEŁYK*
Affiliation:
Institute of Philosophy, University of Warsaw
BARTOSZ WCISŁO*
Affiliation:
Institute of Philosophy, University of Warsaw
*
*INSTITUTE OF PHILOSOPHY UNIVERSITY OF WARSAW WARSAW, POLAND E-mail: [email protected]
†INSTITUTE OF PHILOSOPHY UNIVERSITY OF WARSAW WARSAW, POLAND E-mail: [email protected]
‡INSTITUTE OF PHILOSOPHY UNIVERSITY OF WARSAW WARSAW, POLAND E-mail: [email protected]
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Abstract

We show that a typed compositional theory of positive truth with internal induction for total formulae (denoted by PTtot) is not semantically conservative over Peano arithmetic. In addition, we observe that the class of models of PA expandable to models of PTtot contains every recursively saturated model of arithmetic. Our results point to a gap in the philosophical project of describing the use of the truth predicate in model-theoretic contexts.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 10 , Issue 1 , March 2017 , pp. 187 - 202
Copyright
Copyright © Association for Symbolic Logic 2016 

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References

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