Conservativity for theories of compositional truth via cut elimination
Logic
2013-08-02 v1 Logic in Computer Science
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
Cite
@article{arxiv.1308.0168,
title = {Conservativity for theories of compositional truth via cut elimination},
author = {Graham E. Leigh},
journal= {arXiv preprint arXiv:1308.0168},
year = {2013}
}
Comments
18 pages