It is a classical result that the theory CT^- with the full induction scheme for the formulae containing the truth predicate, called CT, is not conservative over PA. In fact, it proves so called global reflection principle which says that an arbitrary arithmetical sentence provable in PA is true (in the sense of the truth predicate). On the other hand, a theorem by Kotlarski, Krajewski, and Lachlan shows that CT^- is conservative.

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