Hausdorff Nonstandard Extensions - doi: 10.5269/bspm.v20i1-2.7519

Vieri Benci; Marco Forti; Mauro Di Nasso

doi:10.5269/bspm.v20i1-2.7519

Hausdorff Nonstandard Extensions - doi: 10.5269/bspm.v20i1-2.7519

Authors

Vieri Benci Universita' di Pisa
Marco Forti Universita’ di Pisa
Mauro Di Nasso Universit`a di Pisa

DOI:

https://doi.org/10.5269/bspm.v20i1-2.7519

Keywords:

Hausdorff extension, connections with the Stone-Cech compactification \betaX, Hausdorff extensions

Abstract

We introduce the notion of Hausdorff extension of an arbitrary set X and we study the connections with the Stone-Cech 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.