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ON UNSUPERSTABLE THEORIES IN GDST

Part of: Connections with other structures, applications Model theory Set theory

Published online by Cambridge University Press:  06 November 2023

MIGUEL MORENO Open the ORCID record for MIGUEL MORENO [Opens in a new window]
MIGUEL MORENO*
Affiliation:
DEPARTMENT OF MATHEMATICS BAR-ILAN UNIVERSITY RAMAT-GAN 5290002, ISRAEL and INSTITUTE OF MATHEMATICS, UNIVERSITY OF VIENNA VIENNA 1090, AUSTRIA URL: http://u.math.biu.ac.il/~morenom3 URL: http://miguelmath.com
*
E-mail: [email protected]
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Abstract

We study the $\kappa $-Borel-reducibility of isomorphism relations of complete first-order theories by using coloured trees. Under some cardinality assumptions, we show the following: For all theories T and T’, if T is classifiable and T’ is unsuperstable, then the isomorphism of models of T’ is strictly above the isomorphism of models of T with respect to $\kappa $-Borel-reducibility.

Keywords

generalized descriptive set theoryclassification theoryisomorphismEhrenfeucht–Mostowski modelscoloured trees

MSC classification

Primary: 03C45: Classification theory, stability and related concepts 03C55: Set-theoretic model theory 03E15: Descriptive set theory 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
Type
Article
Information
The Journal of Symbolic Logic , Volume 89 , Issue 4 , December 2024 , pp. 1720 - 1746
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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