Sets, the Axiom of Choice, And All That: A Tutorial

TL;DR

This tutorial explains the Axiom of Choice, its equivalences like Zorn's Lemma, and explores its applications in computer science to develop mathematical structures.

Contribution

It provides an accessible overview of the Axiom of Choice and its equivalents, emphasizing their relevance to computer science applications.

Findings

Axiom of Choice is equivalent to Zorn's Lemma and Tuckey's Maximality Principle.

The tutorial highlights the importance of these principles in constructing mathematical structures.

Connections between set theory and computer science are elucidated.

Abstract

This tutorial deal with the Axiom of Choice and some of its applications to topics related to Computer Science. We will see that the Axiom of Choice is equivalent to some well-known proof principles like Zorn's Lemma or Tuckey's Maximality Principle. We try to touch upon some topics, which appear to be important for developing mathematical structures within computer science.