Generalized Descriptive Set Theory and Classification Theory

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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
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.isversionof 978-0-8218-9475-0
dc.relation.isversionof 978-1-4704-1671-3
dc.rights.uri info:eu-repo/semantics/closedAccess
dc.subject 111 Mathematics
dc.subject Matemaattinen logiikka
dc.subject deskriptiivinen joukko-oppi
dc.subject malliteoria
dc.title Generalized Descriptive Set Theory and Classification Theory en
dc.type Book
dc.contributor.organization Department of Mathematics and Statistics
dc.description.reviewstatus Peer reviewed
dc.relation.doi https://doi.org/10.1090/memo/1081
dc.relation.issn 0065-9266
dc.rights.accesslevel closedAccess
dc.type.version submittedVersion
dc.identifier.url http://arxiv.org/abs/1207.4311

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