The isomorphism relation of theories with S-DOP in the generalised Baire spaces

Miguel Moreno

doi:10.1016/j.apal.2021.103044

The isomorphism relation of theories with S-DOP in the generalised Baire spaces

Miguel Moreno

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We study the Borel-reducibility of isomorphism relations in the generalised Baire space κ^κ. In the main result we show for inaccessible κ, that if T is a classifiable theory and T^′ is superstable with the strong dimensional order property (S-DOP), then the isomorphism of models of T is Borel reducible to the isomorphism of models of T^′. In fact we show the consistency of the following: If κ is inaccessible and T is a superstable theory with S-DOP, then the isomorphism of models of T is Σ₁¹-complete.

Original language	English
Article number	103044
Journal	Annals of Pure and Applied Logic
Volume	173
Issue number	2
DOIs	https://doi.org/10.1016/j.apal.2021.103044
State	Published - Feb 2022

Bibliographical note

Publisher Copyright:
© 2021 Elsevier B.V.

Funding

This work was made under the supervision of Tapani Hyttinen. I want to express my gratitude to him for introducing me to the topic, his valuable advices and support during this work. I would like to thank the referees for carefully reading the article and providing comments that improve the readability and quality. This research was supported by the Doctoral Programme in Mathematics and Statistics of the University of Helsinki ( DOMAST ). During the revision and editing of this paper, the author was a postdoc at Bar-Ilan University supported by the European Research Council (grant agreement ERC-2018-StG 802756 ) and was a postdoc at University of Vienna supported by the Vilho, Yrjö and Kalle Väisälä Foundation of the Finnish Academy of Science and Letters , and the Austrian Science Fund FWF, Grant I 3709-N35 .

Funders	Funder number
DOMAST
Helsingin Yliopisto
Horizon 2020 Framework Programme	802756
European Commission
Suomalainen Tiedeakatemia
Austrian Science Fund	I 3709-N35
Universität Wien

Keywords

Classification theory
Dimensional order property
Generalised descriptive set theory
Isomorphism

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10.1016/j.apal.2021.103044

Cite this

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The isomorphism relation of theories with S-DOP in the generalised Baire spaces

Abstract

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Keywords

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