Naive Descriptive Set Theory

TL;DR

This paper provides an accessible introduction to descriptive set theory, covering fundamental concepts and tools for mathematicians without prior logic background, with applications to analysis and dynamical systems.

Contribution

It offers a simplified, beginner-friendly overview of key descriptive set theory topics, bridging the gap for mathematicians from other fields.

Findings

Explains the hierarchy of Borel and analytic sets

Introduces trees, Suslin's operation A, and separation theorems

Provides foundational knowledge for applications in analysis and dynamics

Abstract

The paper is a naive introduction to descriptive set theory. It is aimed mathematicians without a background in logic. The goal is to provide the basic facts used for applications of descriptive set theory to other areas of mathematics, particularly analysis and dynamical systems. The only topological or set theoretic background required is covered in undergraduate courses. It covers the hierarchy of Borel sets and the analytic sets, trees, Suslin's operation A, reductions, norms, separation theorems and uniformization.