کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4662144 1633516 2009 36 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A minimalist two-level foundation for constructive mathematics
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات منطق ریاضی
پیش نمایش صفحه اول مقاله
A minimalist two-level foundation for constructive mathematics
چکیده انگلیسی

We present a two-level theory to formalize constructive mathematics as advocated in a previous paper with G. Sambin.One level is given by an intensional type theory, called Minimal type theory. This theory extends a previous version with collections.The other level is given by an extensional set theory that is interpreted in the first one by means of a quotient model.This two-level theory has two main features: it is minimal among the most relevant foundations for constructive mathematics; it is constructive thanks to the way the extensional level is linked to the intensional one which fulfills the “proofs-as-programs” paradigm and acts as a programming language.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 160, Issue 3, September 2009, Pages 319-354