Omega-powers and descriptive set theory

Dominique Lecomte (1)

1 IMJ - Institut de Mathématiques de Jussieu

We study the sets of the infinite sentences constructible with a dictionary over a finite alphabet, from the viewpoint of descriptive set theory. Among other things, this gives some true co-analytic sets. The case where the dictionary is finite is studied and gives a natural example of a set at the level omega of the Wadge hierarchy.

Keywords: omega-power; Borel class

Domains: Logic [math.LO]; General Topology [math.GN]

Dominique Lecomte. Omega-powers and descriptive set theory. The Journal of Symbolic Logic, 2005, 70 (4), pp.1210-1232. ⟨hal-00175696⟩