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A Categorical Construction of Ultrafilters

Authors
  • Litt, Daniel
  • Abel, Zachary
  • Kominers, Scott D.
Type
Preprint
Publication Date
May 13, 2009
Submission Date
Oct 12, 2007
Identifiers
arXiv ID: 0710.2497
Source
arXiv
License
Yellow
External links

Abstract

Ultrafilters are useful mathematical objects having applications in nonstandard analysis, Ramsey theory, Boolean algebra, topology, and other areas of mathematics. In this note, we provide a categorical construction of ultrafilters in terms of the inverse limit of an inverse family of finite partitions; this is an elementary and intuitive presentation of a consequence of the profiniteness of Stone spaces. We then apply this construction to answer a question of Rosinger posed in arXiv:0709.0084v2 in the negative.

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