2026-09-22T11:18:30Zhttps://iris.polito.it/oai/request

oai:iris.polito.it:11583/30116082026-06-03T09:14:38Zcom_11583_2614433com_11583_2614425col_11583_2614424

Complexity hierarchies in generalized descriptive set theory Pitton, Beatrice Pitton, Beatrice Settore MATH-01/A - Logica matematica Within the framework of generalized descriptive set theory, we conduct a systematic analysis of several hierarchies of classes of sets and functions. At the level of sets, we study the Borel hierarchy, the difference hierarchy, and the Wadge hierarchy; at the level of functions, we examine the Baire class hierarchy as well as the class of Borel-measurable functions. We aim for maximal generality in two directions. First, we adopt a cardinal-independent approach, working with uncountable cardinals κ under the sole assumption that 2<κ = κ, thereby encompassing both regular and singular cardinals. Second, whenever feasible, we move beyond the generalized Cantor and Baire spaces, carrying out the analysis in broader classes of topological spaces. 2026 info:eu-repo/semantics/doctoralThesis https://hdl.handle.net/11583/3011608 eng numberofpages:234 info:eu-repo/semantics/openAccess license:Creative commons license:Creative commons license uri:http://creativecommons.org/licenses/by-nc-nd/4.0/ license uri:http://creativecommons.org/licenses/by-nc-nd/4.0/