Aspects of Choiceless Set Theory

Summary

The Axiom of Choice is one of the most fundamental axioms in modern mathematics, and it is used in almost every field of pure mathematics. The axiom provides us with the existence of certain objects, but not with their description. Sometimes such a description is desirable, in which case we need to understand in depth the use we make of the Axiom of Choice and whether or not it is necessary. The standard techniques come from set theory and they are forcing and symmetric extensions.

In this project the student will advance the knowledge we have about the necessity of the Axiom of Choice in various subjects of mathematics by using and extending these standard techniques.

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