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Ultrafilter on a set

In the mathematical field of set theory, an ultrafilter on a set X {\displaystyle X} is a maximal filter on the set X . {\displaystyle X.} In other words, it is a collection of subsets of X {\displaystyle X} that satisfies the definition of a filter on X {\displaystyle X} and that is maximal with respect to inclusion, in the sense that there does not…

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Overview

Definitions

Generalization to ultra prefilters

Characterizations

Examples, properties, and sufficient conditions

The ultrafilter lemma

Completeness

Ordering on ultrafilters

Ultrafilters on 𝒫(ω)

Bibliography

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Map overview Semantic statistics

Ultrafilter on a set

Nodes130
Edges129
Triples0
Avg. degree1.98
Density0.015385
Components1

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Important terminology

displaystyle ultrafilter set filter every sets lemma ultrafilters subseteq ultra family zf equivalent mathcal theorem subset free finite principal setminus

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SubjectPredicateObjectConfidenceSrc

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