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MOST(?) THEORIES HAVE BOREL COMPLETE REDUCTS
Published online by Cambridge University Press: 27 September 2021
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.
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- © The Author(s), 2021. Published by Cambridge University Press on behalf of The Association for Symbolic Logic