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MODELS OF PT WITH INTERNAL INDUCTION FOR TOTAL FORMULAE

  • CEZARY CIEŚLIŃSKI (a1), MATEUSZ ŁEŁYK (a1) and BARTOSZ WCISŁO (a1)
Abstract
Abstract

We show that a typed compositional theory of positive truth with internal induction for total formulae (denoted by PT tot ) is not semantically conservative over Peano arithmetic. In addition, we observe that the class of models of PA expandable to models of PT tot 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.

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Corresponding author
*INSTITUTE OF PHILOSOPHY UNIVERSITY OF WARSAW WARSAW, POLAND E-mail: c.cieslinski@uw.edu.pl
INSTITUTE OF PHILOSOPHY UNIVERSITY OF WARSAW WARSAW, POLAND E-mail: mlelyk@student.uw.edu.pl
INSTITUTE OF PHILOSOPHY UNIVERSITY OF WARSAW WARSAW, POLAND E-mail: bar.wcislo@gmail.com
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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
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