Nonstandard methods characterize the weak, strong, and mixed extensions of arbitrary relations to ultrafilter spaces and their interplay.
$\widetilde{\mid}\hspace{1mm}$-divisibility of ultrafilters
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abstract
We further investigate a divisibility relation on the set $\beta N$ of ultrafilters on the set of natural numbers. We single out prime ultrafilters (divisible only by 1 and themselves) and establish a hierarchy in which a position of every ultrafilter depends on the set of prime ultrafilters it is divisible by. We also construct ultrafilters with many immediate successors in this hierarchy and find positions of products of ultrafilters.
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2025 1verdicts
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Weak, strong and mixed extensions of relations to spaces of ultrafilters
Nonstandard methods characterize the weak, strong, and mixed extensions of arbitrary relations to ultrafilter spaces and their interplay.