کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4661738 | 1633456 | 2015 | 66 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A new model construction by making a detour via intuitionistic theories I: Operational set theory without choice is Î 1-equivalent to KP
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
منطق ریاضی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: A new model construction by making a detour via intuitionistic theories I: Operational set theory without choice is Î 1-equivalent to KP A new model construction by making a detour via intuitionistic theories I: Operational set theory without choice is Î 1-equivalent to KP](/preview/png/4661738.png)
چکیده انگلیسی
We introduce a version of operational set theory, OSTâ, without a choice operation, which has a machinery for Î0 separation based on truth functions and the separation operator, and a new kind of applicative set theory, so-called weak explicit set theory WEST, based on Gödel operations. We show that both the theories and Kripke-Platek set theory KP with infinity are pairwise Î 1 equivalent. We also show analogous assertions for subtheories with â-induction restricted in various ways and for supertheories extended by powerset, beta, limit and Mahlo operations. Whereas the upper bound is given by a refinement of inductive definition in KP, the lower bound is by a combination, in a specific way, of realisability, (intuitionistic) forcing and negative interpretations. Thus, despite interpretability between classical theories, we make “a detour via intuitionistic theories”. The combined interpretation, seen as a model construction in the sense of Visser's miniature model theory, is a new way of construction for classical theories and could be said the third kind of model construction ever used which is non-trivial on the logical connective level, after generic extension à la Cohen and Krivine's classical realisability model.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 166, Issue 2, February 2015, Pages 121-186
Journal: Annals of Pure and Applied Logic - Volume 166, Issue 2, February 2015, Pages 121-186
نویسندگان
SATO Kentaro, Rico Zumbrunnen,