Forti, Marco; Di Nasso, Mauro; Benci, Vieri Hausdorff nonstandard extensions. (English) Zbl 1061.54018 Bol. Soc. Parana. Mat. (3) 20, No. 1-2, 9-20 (2002). 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. Reviewer: T. Thrivikraman (Cochin) Cited in 4 Documents 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 Keywords:hypernatural numbers; Hausdorff extension; Stone-Čech compactification PDFBibTeX XMLCite \textit{M. Forti} et al., Bol. Soc. Parana. Mat. (3) 20, No. 1--2, 9--20 (2002; Zbl 1061.54018)