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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We examine the reverse-mathematical strength of several theorems in classical and effective model theory concerning first-order theories and their number of models. We prove that, among these, most are equivalent to one of the familiar systems RCA0, WKL0, or ACA0. We are led to a purely model-theoretic statement that implies WKL0 but refutes ACA0 over RCA0.
متن کاملReverse Mathematics
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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ژورنال
عنوان ژورنال: BRICS Report Series
سال: 2000
ISSN: 1601-5355,0909-0878
DOI: 10.7146/brics.v7i49.20216