Zorn's Lemma

Summary

Zorn's Lemma states that if every chain in a partially ordered set S has an upper bound, then S has a maximal element. Zorn's Lemma is equivalent to the Axiom of Choice.

Context

This concept has the prerequisites:

Goals

  • Know the statement of Zorn's Lemma
  • Be aware that it is equivalent to the Axiom of Choice
  • Prove Zorn's Lemma, assuming the Axiom of Choice
  • Prove the Axiom of Choice using Zorn's Lemma
  • Use Zorn's Lemma to show that every vector space has a basis

Core resources (read/watch one of the following)

-Free-

Notes on Set Theory (2013)
Lecture notes for a course on axiomatic set theory.
Author: Henry Cohn

-Paid-

See also

-No Additional Notes-