Topological and Arithmetical Properties of Infinitary Rational Relations

Olivier Finkel (1)

1 ELM - Équipe de Logique Mathématique

We study the topological complexity of infinitary rational relations, with regard to the Borel and projective hierarchies. In particular we show that there exists some infinitary rational relations which are analytic but non Borel sets hence also non arithmetical sets, giving an answer to a question of Simonnet [Automates et théorie descriptive, Ph. D. Thesis, Université Paris 7, March 1992]. We then deduce the undecidability of numerous topological and arithmetical properties of infinitary rational relations.

Domaines: Logique en informatique [cs.LO]; Logique [math.LO]

Olivier Finkel. Topological and Arithmetical Properties of Infinitary Rational Relations. 2002, 13 p. ⟨hal-00114323⟩