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arXiv · 2103.09724

Most(?) theories have Borel complete reducts

Michael C. Laskowski·Douglas S. Ulrich
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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 1-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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Michael C. Laskowski, Douglas S. Ulrich. 2021-03-17. Most(?) theories have Borel complete reducts. https://arxiv.org/abs/2103.09724

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