25.Indeed, more is true. Not even the theory
TB, which consists of
PA (with truth allowed in the induction scheme) plus the Tarski-Biconditional sentences of the form
$T(\overline{{g(A)}} )\, \leftrightarrow \,A$
, where
A ranges over arithmetical sentences and
g is the function that assigns Gödel codes to sentences, is semantically conservative over
PA. See A. Strollo (2013) Deflationism and the invisible power of truth.
Dialectica,
67, pp.
521–
543.
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