Shavrukov, V. Yu. Interpreting reflexive theories in finitely many axioms. (English) Zbl 0874.03066 Fundam. Math. 152, No. 2, 99-116 (1997). 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. Cited in 2 Documents MSC: 03F25 Relative consistency and interpretations 03F30 First-order arithmetic and fragments Keywords:relative interpretability; finitely axiomatized sequential theories; reflexive theories; provability of restricted consistency statements on cuts PDFBibTeX XMLCite \textit{V. Yu. Shavrukov}, Fundam. Math. 152, No. 2, 99--116 (1997; Zbl 0874.03066) Full Text: EuDML