کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4661849 | 1633464 | 2014 | 33 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
CZF does not have the existence property
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
منطق ریاضی
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
Constructive theories usually have interesting metamathematical properties where explicit witnesses can be extracted from proofs of existential sentences. For relational theories, probably the most natural of these is the existence property, EP, sometimes referred to as the set existence property. This states that whenever (âx)Ï(x) is provable, there is a formula Ï(x) such that (â!x)Ï(x)â§Ï(x) is provable. It has been known since the 80s that EP holds for some intuitionistic set theories and yet fails for IZF. Despite this, it has remained open until now whether EP holds for the most well known constructive set theory, CZF. In this paper we show that EP fails for CZF.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 165, Issue 5, May 2014, Pages 1115-1147
Journal: Annals of Pure and Applied Logic - Volume 165, Issue 5, May 2014, Pages 1115-1147
نویسندگان
Andrew W. Swan,