Title: An Effective Construction of a Free z-ultrafilter
Abstract:ABSTRACT: It is known that free ultrafilters cannot be constructed effectively (i.e., in ZF set theory without any additional choice principle). In this paper a nonconvergent, thus free, z ‐ultrafilte...ABSTRACT: It is known that free ultrafilters cannot be constructed effectively (i.e., in ZF set theory without any additional choice principle). In this paper a nonconvergent, thus free, z ‐ultrafilter is constructed effectively in a suitable zero‐dimensional topological space X . Thus the implication C ‐compact ? B ‐compact (which under AC is an equivalence for completely regular spaces) fails to be an equivalence in ZF even for zero‐dimensional spaces, where B ‐compact (respectively, C ‐compact) means that every ultrafilter (respectively, z ‐ultrafilter) converges.Read More
Publication Year: 1996
Publication Date: 1996-12-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 1
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