Hausdorff Nonstandard Extensions

Abstract

We introduce the notion of Hausdorff extension of an arbitrary set Xand 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.

Keywords

• Hausdorff extension
• Stone-Cech compactification.