Ultrafilters in reverse mathematics
نویسندگان
چکیده
منابع مشابه
Non-principal Ultrafilters, Program Extraction and Higher Order Reverse Mathematics
We investigate the strength of the existence of a non-principal ultrafilter over fragments of higher order arithmetic. Let (U) be the statement that a non-principal ultrafilter on N exists and let ACA0 be the higher order extension of ACA0. We show that ACA0 + (U) is Π2-conservative over ACA0 and thus that ACA0 +(U) is conservative over PA. Moreover, we provide a program extraction method and s...
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An important open problem in Reverse Mathematics ([16, 25]) is the reduction of the first-order strength of the base theory from IΣ1 to I∆0 + exp. The system ERNA, a version of Nonstandard Analysis based on the system I∆0 + exp, provides a partial solution to this problem. Indeed, Weak König’s lemma and many of its equivalent formulations from Reverse Mathematics can be ‘pushed down’ into ERNA,...
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In math we typically assume a set of axioms to prove a theorem. In reverse mathematics, the premise is reversed: we start with a theorem and try to determine the minimal axiomatic system required to prove the theorem (over a weak base system). This produces interesting results, as it can be shown that theorems from different fields of math such as group theory and analysis are in fact equivalen...
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The basic reference for reverse mathematics is my recently published book Subsystems of Second Order Arithmetic [32]. The web site for the book is www.math.psu.edu/simpson/sosoa/. This article is a write-up of some representative open problems in reverse mathematics. It was originally a handout for my 45-minute invited talk at the AMS-INS-SIAM conference Computability Theory and Applications, J...
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The objective of this paper is to provide a source of open questions in reverse mathematics and to point to areas where there could be interesting developments. The questions I discuss are mostly known and come from somewhere in the literature. My objective was to compile them in one place and discuss them in the context of related work. The list is definitely not comprehensive, and my choice o...
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ژورنال
عنوان ژورنال: Journal of Mathematical Logic
سال: 2014
ISSN: 0219-0613,1793-6691
DOI: 10.1142/s0219061314500019