MOST(?) THEORIES HAVE BOREL COMPLETE REDUCTS
MOST(?) THEORIES HAVE BOREL COMPLETE REDUCTS
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 …