Separation of analytic sets by rectangles of low complexity

TL;DR

This paper develops tests to determine when disjoint analytic sets can be separated by low-complexity rectangles, advancing understanding in descriptive set theory.

Contribution

It introduces Hurewicz tests for separating disjoint analytic sets using rectangles of specific low complexity classes.

Findings

Provides criteria for separation of analytic sets by low-complexity rectangles

Establishes Hurewicz tests applicable to various classes of sets

Enhances methods for analyzing set separation in descriptive set theory

Abstract

We provide Hurewicz tests for the separation of disjoint analytic sets by rectangles of the form $\Gamma\times\Gamma'$ for $\Gamma,\Gamma'\in {\mathbf\Sigma^0_1 , \mathbf\Pi^0_1 , \mathbf\Pi^0_2 }$.