Group Structure on Arbitrary Sets: An Algebraic Application of the Axiom of Choice
In 1972 Hajnal and Kertész published a paper proving that the Axiom of Choice is equivalent to the assertion that a groupoid structure can be defined on every set. This thesis aims to provide the necessary background needed for this proof. In the first part basic concepts in set theory such as the Well-Ordering Theorem are derived. This culminates in a lemma by Hartogs (1915) in which it is shown,
