The set-theorist's real numbers

Abstract

Descriptive set theorists often refer to elements of the Baire space, $\mathcal{N}={}^{\omega }\omega$, as ``reals.'' In this expository article, we present mathematical justification for this practice and highlight the advantages of working with $\mathcal{N}$ over $\mathbb{R}$ in the context of descriptive set theory.

arXiv comment18 pages