کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4661936 1633475 2013 14 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Reverse-engineering Reverse Mathematics
ترجمه فارسی عنوان
مهندسی معکوس ریاضیات معکوس ☆
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات منطق ریاضی
چکیده انگلیسی

An important open problem in Reverse Mathematics (Montalbán, 2011 [16], ; Simpson, 2009 [25], ) is the reduction of the first-order strength of the base theory from IΣ1 to IΔ0+exp. The system ERNA, a version of Nonstandard Analysis based on the system IΔ0+exp, provides a partial solution to this problem. Indeed, weak Königʼs lemma and many of its equivalent formulations from Reverse Mathematics can be ‘pushed down’ into ERNA, while preserving the equivalences, but at the price of replacing equality with ‘≈’, i.e. infinitesimal proximity (Sanders, 2011 [19], ). The logical principle corresponding to weak Königʼs lemma is the universal transfer principle from Nonstandard Analysis. Here, we consider the intermediate and mean value theorem and their uniform generalizations. We show that ERNAʼs Reverse Mathematics mirrors the situation in classical Reverse Mathematics. This further supports our claim from Sanders (2011) [19] that the Reverse Mathematics of ERNA plus universal transfer is a copy up to infinitesimals of that of WKL0. We discuss some of the philosophical implications of our results.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 164, Issue 5, May 2013, Pages 528-541