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math.LO2021
Characterizing the existence of a Borel complete expansion
Michael C. Laskowski, Douglas S. Ulrich
We develop general machinery to cast the class of potential canonical Scott sentences of an infinitary sentence as a class of structures in a related language. From this, we sh…
math.LO2021
Most(?) theories have Borel complete reducts
Michael C. Laskowski, Douglas S. Ulrich
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 re…