Journal directory listing - Volume 11-20 (1966-1975) - Volume 14 (1969)
Axiom of Choice Synopsis
Author: Fun-Pay Kuo
Abstract：
In axiomatic set theory, Axiom of Choice is not easier to apply than other axioms. We often use some axioms which are equivelent to Axiom of Choice. In this note we shall prove two useful axioms. Zorn's Lemma and Well-ordering Postulate which are equivalent to Axiom of Choice and give two examples to show their applications. We shall use Well-ordering Postulate to prove that any subgroup of a free abelian group is free and Zorn's Lemma to show that any vector space over a field has a basis.