Generalized Descriptive Set Theory and Classification Theory
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dc.contributor.author |
Friedman, Sy-David |
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dc.contributor.author |
Hyttinen, Tapani |
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dc.contributor.author |
Kulikov, Vadim |
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dc.date.accessioned |
2015-11-09T08:59:02Z |
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dc.date.available |
2015-11-09T08:59:02Z |
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dc.date.issued |
2014 |
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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 |
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dc.identifier.other |
PURE: 55141368 |
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dc.identifier.other |
PURE UUID: ab647981-e58a-4ea2-bf9c-90c8c2ec2739 |
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dc.identifier.other |
WOS: 000348306100001 |
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dc.identifier.other |
ORCID: /0000-0002-5125-3839/work/38048495 |
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dc.identifier.uri |
http://hdl.handle.net/10138/157923 |
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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 |
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dc.publisher |
American Mathematical Society |
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dc.relation.ispartofseries |
Memoirs of the American Mathematical Society |
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dc.relation.isversionof |
978-0-8218-9475-0 |
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dc.relation.isversionof |
978-1-4704-1671-3 |
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dc.rights.uri |
info:eu-repo/semantics/closedAccess |
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dc.subject |
111 Mathematics |
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dc.subject |
Matemaattinen logiikka |
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dc.subject |
deskriptiivinen joukko-oppi |
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dc.subject |
malliteoria |
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dc.title |
Generalized Descriptive Set Theory and Classification Theory |
en |
dc.type |
Book |
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dc.contributor.organization |
Department of Mathematics and Statistics |
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dc.description.reviewstatus |
Peer reviewed |
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dc.relation.doi |
https://doi.org/10.1090/memo/1081 |
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dc.relation.issn |
0065-9266 |
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dc.rights.accesslevel |
closedAccess |
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dc.type.version |
submittedVersion |
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dc.identifier.url |
http://arxiv.org/abs/1207.4311 |
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