Compositional truth with propositional tautologies and quantifier-free correctness
Logic
2020-11-16 v1
Abstract
Cie\'sli\'nski asked whether compositional truth theory with the additional axiom that all propositional tautologies are true is conservative over Peano Arithmetic. We provide a partial answer to this question, showing that if we additionally assume that truth predicate agrees with arithmetical truth on quantifier-free sentences, the resulting theory is as strong as -induction for the compositional truth predicate, hence non-conservative. On the other hand, it can be shown with a routine argument that the principle of quantifier-free correctness is itself conservative.
Cite
@article{arxiv.2011.06940,
title = {Compositional truth with propositional tautologies and quantifier-free correctness},
author = {Bartosz Wcisło},
journal= {arXiv preprint arXiv:2011.06940},
year = {2020}
}