On the Topological Complexity of Infinitary Rational Relations

TL;DR

This paper demonstrates that certain infinitary rational relations can be analytic but non-Borel, revealing complex topological properties of these relations and answering a long-standing question in descriptive set theory.

Contribution

It establishes the existence of infinitary rational relations with non-Borel complexity, advancing understanding of their topological and descriptive set-theoretic properties.

Findings

Existence of non-Borel infinitary rational relations

Answer to Simonnet’s 1992 question

Insight into the topological complexity of rational relations

Abstract

We prove in this paper that there exists some infinitary rational relations which are analytic but non Borel sets, giving an answer to a question of Simonnet [Automates et Th\'eorie Descriptive, Ph. D. Thesis, Universit\'e Paris 7, March 1992].