Classical determinate truth without induction

TL;DR

This paper demonstrates that a classical, type-free truth theory without induction is conservative over Peano Arithmetic, advancing understanding of truth theories in logic.

Contribution

It shows that the induction-free variant of Fujimoto and Halbach's truth theory is conservative over Peano Arithmetic, providing new insights into classical truth without induction.

Findings

Induction-free variant is conservative over Peano Arithmetic

Supports full classical compositional clauses for connectives and quantifiers

Advances understanding of truth theories without induction

Abstract

Fujimoto and Halbach had introduced a novel theory of type-free truth CD which satisfies full classical compositional clauses for connectives and quantifiers. Answering their question, we show that the induction-free variant of that theory is conservative over Peano Arithmetic.