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CONSERVATIVITY FOR THEORIES OF COMPOSITIONAL TRUTH VIA CUT ELIMINATION

Published online by Cambridge University Press:  22 July 2015

GRAHAM E. LEIGH
GRAHAM E. LEIGH*
Affiliation:
INSTITUTE OF DISCRETE MATHEMATICS AND GEOMETRY VIENNA UNIVERSITY OF TECHNOLOGY WIEDNER HAUPTSTRAßE 8–10 1040 VIENNA, AUSTRIAE-mail: graham.leigh@tuwien.ac.at
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Abstract

We present a cut elimination argument that witnesses the conservativity of the compositional axioms for truth (without the extended induction axiom) over any theory interpreting a weak subsystem of arithmetic. In doing so we also fix a critical error in Halbach’s original presentation. Our methods show that the admission of these axioms determines a hyper-exponential reduction in the size of derivations of truth-free statements.

Keywords

proof theorycut eliminationaxiomatic truthcompositional theory of truth
Type
Articles
Information
The Journal of Symbolic Logic , Volume 80 , Issue 3 , September 2015 , pp. 845 - 865
Copyright
Copyright © The Association for Symbolic Logic 2015 

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