Complexity hierarchies in generalized descriptive set theory

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.

Author dc:creator

• Pitton, Beatrice

• Settore MATH-01/A - Logica matematica

Statement dc:rights

• info:eu-repo/semantics/openAccess
• license:Creative commons
• license uri:http://creativecommons.org/licenses/by-nc-nd/4.0/

Language dc:language

eng

Handle dc:identifier

https://hdl.handle.net/11583/3011608

OAI identifier oai:identifier

oai:iris.polito.it:11583/3011608