Notes on bounded induction for the compositional truth predicate
Mateusz {\L}e{\l}yk, Bartosz Wcis{\l}o
TL;DR
This paper demonstrates that certain theories of the compositional truth predicate extend Peano Arithmetic and can prove the global reflection principle, highlighting their non-conservativity and strength.
Contribution
It proves the non-conservativity of the extensional compositional truth theory over Peano Arithmetic and shows that a modified theory can prove the global reflection principle.
Findings
The theory of the compositional truth predicate is not conservative over PA.
A modified truth theory proves the global reflection principle.
The results clarify the strength of truth theories in arithmetic.
Abstract
We prove that the theory of the extensional compositional truth predicate for the language of arithmetic with -induction scheme for the truth predicate and the full arithmetical induction scheme is not conservative over Peano Arithmetic. In addition, we show that a slightly modified theory of truth actually proves the global reflection principle over the base theory.
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