| ˜ -Divisibility of ultrafilters

Annals of Pure and Applied Logic 172 (1):102857 (2021)
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Abstract

We further investigate a divisibility relation on the set of BN 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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Citations of this work

More about divisibility in βN.Boris Šobot - 2021 - Mathematical Logic Quarterly 67 (1):77-87.
Multiplicative finite embeddability vs divisibility of ultrafilters.Boris Šobot - 2022 - Archive for Mathematical Logic 61 (3):535-553.
Congruence of ultrafilters.Boris Šobot - 2021 - Journal of Symbolic Logic 86 (2):746-761.

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References found in this work

The Theory of Ultrafilters.W. W. Comfort & S. Negrepontis - 1976 - Journal of Symbolic Logic 41 (4):782-783.

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