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Full Idea
Compositional Truth CT proves the consistency of Peano arithmetic, which is not provable in Peano arithmetic by Gödel's second incompleteness theorem. Hence the theory CT is not conservative over Peano arithmetic.
Gist of Idea
CT proves PA consistent, which PA can't do on its own, so CT is not conservative over PA
Source
Volker Halbach (Axiomatic Theories of Truth [2011], 8.6)
Book Ref
Halbach,Volker: 'Axiomatic Theories of Truth' [CUP 2011], p.106
Related Ideas
Idea 16318 Compositional Truth CT has the truth of a sentence depending of the semantic values of its constituents [Halbach]
Idea 10122 Second Incompleteness: a decent consistent system can't prove its own consistency [Gödel, by George/Velleman]
Idea 16313 A theory is 'conservative' if it adds no new theorems to its base theory [Halbach, by PG]