A new model construction by making a detour via intuitionistic theories II: Interpretability lower bound of Feferman's explicit mathematics T0

TitleA new model construction by making a detour via intuitionistic theories II: Interpretability lower bound of Feferman's explicit mathematics T0
Publication TypeJournal Article
Year of Publication2015
AuthorsSato, K
JournalAnnals of pure and applied logic
Volume166
Pagination800-835
AbstractWe partially solve a long-standing problem in the proof theory of explicit mathematics or the proof theory in general. Namely, we give a lower bound of Feferman?s system T0 of explicit mathematics (but only when formulated on classical logic) with a concrete interpretat ion of the subsystem {$Σ$}12-AC+ (BI) of second order arithmetic inside T0. Whereas a lower bound proof in the sense of proof-theoretic reducibility or of ordinalanalysis was already given in 80s, the lower bound in the sense of interpretability we give here is new. We apply the new interpretation method developed by the author and Zumbrunnen (2015), which can be seen as the third kind of model construction method for classical theories, after Cohen?s forcing and Krivine?s classical realizability. It gives us an interpretation between classical theories, by composing interpretations between intuitionistic theories.
URLhttp://www.iam.unibe.ch/ltgpub/2015/sat15b.pdf