Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4661795 | Annals of Pure and Applied Logic | 2013 | 19 Pages |
Abstract
The paper aims to provide precise proof theoretic characterizations of Myhill-Friedman-style “weak” constructive extensional set theories and Aczel-Rathjen analogous constructive set theories both enriched by Mostowski-style collapsing axioms and/or related anti-foundation axioms. The main results include full intuitionistic conservations over the corresponding purely arithmetical formalisms that are well known in the reverse mathematics - which strengthens analogous results obtained by the author in the 80s. The present research was inspired by the more recent Sato-style “weak weak” classical extensional set theories whose proof theoretic strengths are shown to strongly exceed the ones of the intuitionistic counterparts in the presence of the collapsing axioms.
Related Topics
Physical Sciences and Engineering
Mathematics
Logic
Authors
Lev Gordeev,