Generalized Descriptive Set Theory and Classification Theory

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dc.contributor University of Helsinki, Department of Mathematics and Statistics en
dc.contributor University of Helsinki, Department of Mathematics and Statistics en
dc.contributor.author Friedman, Sy-David
dc.contributor.author Hyttinen, Tapani
dc.contributor.author Kulikov, Vadim
dc.date.accessioned 2015-11-09T08:59:02Z
dc.date.available 2015-11-09T08:59:02Z
dc.date.issued 2014
dc.identifier.citation Friedman , S-D , Hyttinen , T & Kulikov , V 2014 , Generalized Descriptive Set Theory and Classification Theory . Memoirs of the American Mathematical Society , no. 1081 , vol. 230 , American Mathematical Society . https://doi.org/10.1090/memo/1081 en
dc.identifier.isbn 978-0-8218-9475-0
dc.identifier.isbn 978-1-4704-1671-3
dc.identifier.other PURE: 55141368
dc.identifier.other PURE UUID: ab647981-e58a-4ea2-bf9c-90c8c2ec2739
dc.identifier.other WOS: 000348306100001
dc.identifier.other ORCID: /0000-0002-5125-3839/work/38048495
dc.identifier.uri http://hdl.handle.net/10138/157923
dc.description.abstract The field of descriptive set theory is mainly concerned with studying subsets of the space of all countable binary sequences. In this paper we study the generalization where countable is replaced by uncountable. We explore properties of generalized Baire and Cantor spaces, equivalence relations and their Borel reducibility. The study shows that the descriptive set theory looks very dierent in this generalized setting compared to the classical, countable case. We also draw the connection between the stability theoretic complexity of first-order theories and the descriptive set theoretic complexity of their isomorphism relations. Our results suggest that Borel reducibility on uncountable structures is a model theoretically natural way to compare the complexity of isomorphism relations. fi
dc.language.iso eng
dc.publisher American Mathematical Society
dc.relation.ispartofseries Memoirs of the American Mathematical Society
dc.relation.uri http://arxiv.org/abs/1207.4311
dc.rights en
dc.subject 111 Mathematics en
dc.subject Matemaattinen logiikka en
dc.subject deskriptiivinen joukko-oppi en
dc.subject malliteoria en
dc.title Generalized Descriptive Set Theory and Classification Theory en
dc.type Book
dc.identifier.doi https://doi.org/10.1090/memo/1081
dc.type.uri info:eu-repo/semantics/other
dc.contributor.pbl

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