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Interpreting reflexive theories in finitely many axioms. (English) Zbl 0874.03066

Summary: For finitely axiomatized sequential theories \(F\) and reflexive theories \(R\), we give a characterization of the relation ‘\(F\) interprets \(R\)’ in terms of provability of restricted consistency statements on cuts. This characterization is used in a proof that the set of \(\Pi_1\) (as well as \(\Sigma_1\)) sentences \(\pi\) such that GB interprets \(\text{ZF}+\pi\) is \(\Sigma^0_3\)-complete.

MSC:

03F25 Relative consistency and interpretations
03F30 First-order arithmetic and fragments
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