There may be no Hausdorff ultrafilters
Tomek Bartoszynski, Saharon Shelah
TL;DR
This paper demonstrates the consistency of the non-existence of Hausdorff ultrafilters, a special class of ultrafilters characterized by a unique functional property.
Contribution
It proves the consistency that no Hausdorff ultrafilters exist, addressing a longstanding question in ultrafilter theory.
Findings
It is consistent that Hausdorff ultrafilters do not exist.
The paper establishes a model where all ultrafilters are non-Hausdorff.
Provides insights into the structure of ultrafilters under certain set-theoretic assumptions.
Abstract
An ultrafilter U is Hausdorff if for any two functions f,g mapping N to N, f(U)=g(U) iff f(n)=g(n) for n in some X in U. We will show that it is consistent that there are no Hausdorff ultrafilters.
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Taxonomy
TopicsMathematical and Theoretical Analysis · Advanced Topology and Set Theory · Computability, Logic, AI Algorithms