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

Sato, Kentaro (2015). A new model construction by making a detour via intuitionistic theories II: Interpretability lower bound of Feferman's explicit mathematics T0. Annals of pure and applied logic, 166(7-8), pp. 800-835. Elsevier 10.1016/j.apal.2015.04.002

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We 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 Σ12-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.

Item Type: Journal Article (Original Article)
Division/Institute: 08 Faculty of Science > Institute of Computer Science (INF) > Logic and Theory Group (LTG)
08 Faculty of Science > Institute of Computer Science (INF)
UniBE Contributor: Sato, Kentaro
Subjects: 000 Computer science, knowledge & systems
500 Science > 510 Mathematics
ISSN: 0168-0072
Publisher: Elsevier
Language: English
Submitter: Florian Ranzi
Date Deposited: 21 May 2015 13:14
Last Modified: 25 May 2015 04:13
Publisher DOI: 10.1016/j.apal.2015.04.002
BORIS DOI: 10.7892/boris.68827
URI: http://boris.unibe.ch/id/eprint/68827

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