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MOST(?) THEORIES HAVE BOREL COMPLETE REDUCTS

Part of: Model theory Set theory

Published online by Cambridge University Press:  27 September 2021

MICHAEL C. LASKOWSKI  and
DOUGLAS S. ULRICH
MICHAEL C. LASKOWSKI*
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF MARYLAND COLLEGE PARK, MD, USA E-mail: ds_ulrich@hotmail.com
DOUGLAS S. ULRICH
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF MARYLAND COLLEGE PARK, MD, USA E-mail: ds_ulrich@hotmail.com
*
E-mail: laskow@umd.edu
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Abstract

We prove that many seemingly simple theories have Borel complete reducts. Specifically, if a countable theory has uncountably many complete one-types, then it has a Borel complete reduct. Similarly, if $Th(M)$ is not small, then $M^{eq}$ has a Borel complete reduct, and if a theory T is not $\omega $ -stable, then the elementary diagram of some countable model of T has a Borel complete reduct.

Keywords

Borel complexitycountable modelsreducts

MSC classification

Primary: 03C50: Models with special properties (saturated, rigid, etc.)
Secondary: 03E15: Descriptive set theory
Type
Article
Information
The Journal of Symbolic Logic , Volume 88 , Issue 1 , March 2023 , pp. 418 - 426
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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References

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