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Hausdorff nonstandard extensions. (English) Zbl 1061.54018

Authors’ abstract: We introduce the notion of Hausdorff extension of an arbitrary set \(X\) and we study the connections with the Stone-Čech compactification \(\beta X\) of the discrete space \(X\). We characterize those Hausdorff extensions that satisfy the “transfer principle” of nonstandard analysis, and we investigate the consistency strength of their existence.

MSC:

54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)
03H05 Nonstandard models in mathematics
03C20 Ultraproducts and related constructions
54D80 Special constructions of topological spaces (spaces of ultrafilters, etc.)
54J05 Nonstandard topology
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