We study the sets of the infinite sentences constructible with a dictionary over a finite alphabet, from the viewpoint of descriptive set theory. Among others, 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 level ω of the Wadge hierarchy.
"ω-powers and descriptive set theory." J. Symbolic Logic 70 (4) 1210 - 1232, December 2005. https://doi.org/10.2178/jsl/1129642123