{"id":{"repo_id":"poli-torino","oai_identifier":"oai:iris.polito.it:11583/3011608"},"canonical_url":"https://search.dev.ndltd.org/etd/poli-torino/oai:iris.polito.it:11583/3011608","repository":{"repo_id":"poli-torino","name":"Politecnico di Torino","base_url":"https://iris.polito.it/oai/request"},"display":{"title":"Complexity hierarchies in generalized descriptive set theory","abstract":"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.","abstract_html":"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&lt;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.","abstract_has_math":false,"creators":["Pitton, Beatrice"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2026,"date_issued":"2026","date_published":"2026","updated_at":"2026-07-24T03:50:39Z","subjects":["Settore MATH-01/A - Logica matematica"],"languages":["eng"],"rights":["info:eu-repo/semantics/openAccess","license:Creative commons","license uri:http://creativecommons.org/licenses/by-nc-nd/4.0/"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/11583/3011608","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Pitton, Beatrice"]},{"key":"dc:creator","label":"Author","values":["Pitton, Beatrice"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2026"]},{"key":"dc:relation","label":"Dc Relation","values":["numberofpages:234"]},{"key":"dc:type","label":"Dc Type","values":["info:eu-repo/semantics/doctoralThesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Settore MATH-01/A - Logica matematica"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["info:eu-repo/semantics/openAccess","license:Creative commons","license uri:http://creativecommons.org/licenses/by-nc-nd/4.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/11583/3011608"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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."]},{"key":"dc:title","label":"Title","values":["Complexity hierarchies in generalized descriptive set theory"]}]}],"canonical_facts":{"dc:contributor":["Pitton, Beatrice"],"dc:creator":["Pitton, Beatrice"],"dc:date":["2026"],"dc:description":["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."],"dc:identifier":["https://hdl.handle.net/11583/3011608"],"dc:language":["eng"],"dc:relation":["numberofpages:234"],"dc:rights":["info:eu-repo/semantics/openAccess","license:Creative commons","license uri:http://creativecommons.org/licenses/by-nc-nd/4.0/"],"dc:subject":["Settore MATH-01/A - Logica matematica"],"dc:title":["Complexity hierarchies in generalized descriptive set theory"],"dc:type":["info:eu-repo/semantics/doctoralThesis"]},"updated_at":"2026-07-24T03:50:39Z"}