Interpreting reflexive theories in finitely many axioms
Tom 152 / 1997
Fundamenta Mathematicae 152 (1997), 99-116 DOI: 10.4064/fm_1997_152_2_1_99_116
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 $∏_1$ (as well as $∑_1$) sentences π such that GB interprets ZF+π is $Σ^0_3$-complete.