Submission date: 17 March 2021

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 ω-stable, then the elementary diagram of some countable model of T has a Borel complete reduct.

Mathematics Subject Classification: 03C50

Keywords and phrases:

Full text arXiv 2103.09724: pdf, ps.