Ultrafilters On A Nonstandard Set
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Date
2011
Department
Mathematics
Program
Master of Arts
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This item is made available by Morgan State University for personal, educational, and research purposes in accordance with Title 17 of the U.S. Copyright Law. Other uses may require permission from the copyright owner.
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Abstract
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.