Most(?) Theories Have Borel Complete Reducts

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Journal of Symbolic Logic 88 (1):418-426 (2023)
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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.

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10.1017/jsl.2021.78

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