ultrafilters (under construction)


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This concept is still under construction.


This concept has the prerequisites:


  • Define filter
  • Define ultrafilter
  • Define principal ultrafilter
  • Give an example of a non-principal ultrafilter
  • Using Zorn's Lemma, show that every filter is contained in an ultrafilter
  • Show that in the case of Boolean algebras, ultrafilters are equivalent to homomorphisms to {0, 1}.

Core resources (read/watch one of the following)


Notes on Logic (2013)
Lecture notes for a course on first order logic.
Location: Section 13, "Filters and ultrafilters," pages 30-33
Author: Henry Cohn


See also

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