Generalized Descriptive Set Theory and Classification Theory

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Pysyväisosoite

http://hdl.handle.net/10138/157923

Lähdeviite

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

Julkaisun nimi: Generalized Descriptive Set Theory and Classification Theory
Tekijä: Friedman, Sy-David; Hyttinen, Tapani; Kulikov, Vadim
Muu tekijä: University of Helsinki, Department of Mathematics and Statistics
University of Helsinki, Department of Mathematics and Statistics
Julkaisija: American Mathematical Society
Päiväys: 2014
Kieli: eng
Kuuluu julkaisusarjaan: Memoirs of the American Mathematical Society
ISBN: 978-0-8218-9475-0
978-1-4704-1671-3
URI: http://hdl.handle.net/10138/157923
Tiivistelmä: 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.
Avainsanat: 111 Mathematics
Matemaattinen logiikka
deskriptiivinen joukko-oppi
malliteoria
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