Ultrafilters On A Nonstandard Set
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With an infinite set X, we have βX, the collection of all ultrafilters on X. We construct a nonstardard model of X(denoted by *X ) and a nonstandard model of βX(denoted by *βX). With β[*X] being the set of all ultrafilters on *X, we explore the relationship between *βX and β[*X]. In this paper we actually discover that elements of *βX are not ultrafilters on *X. In other words, the set *β and the set β[*X] have no common elements.