Linked from

The 10 pages that link to Ultrafilter, each with the reason it gives.

• Compactness theoremBroader topic: The ultraproduct proof uses an ultrafilter containing sets of indices where each sentence holds.

• Arrow's impossibility theoremRelated: In a standard proof, decisive coalitions form an ultrafilter, which must be concentrated on one individual.

• Zorn's lemmaBroader topic: Zorn's lemma extends suitable proper filters to ultrafilters.

• Stone–Čech compactificationRelated: Ultrafilters on X provide a concrete model for points of βX when X is discrete.

• Tychonoff's theoremRelated: Convergence of ultrafilters gives a compactness-based formulation and proof.

• Hyperreal numberRelated: A nonprincipal ultrafilter determines which sequences count as equivalent in the ultrapower construction.

• Large cardinalRelated: A suitably complete ultrafilter provides the measure that defines a measurable cardinal.

• Boolean prime ideal theoremBroader topic: A maximal proper filter yields a prime ideal by taking its complement.

• Stone's representation theorem for Boolean algebrasRelated: Points of the Stone space are the Boolean algebra's ultrafilters.

• Teichmüller–Tukey lemmaBroader topic: Maximality principles derived from the lemma can extend filters to ultrafilters.