4 papers · 1 filter
Borel completeness of -modules when fails the DCC on pp-definable subgroups
Michael C. Laskowski, Danielle S. Ulrich
We prove that for any countable ring (not necessarily commutative), if the associated left -module has a strictly descending sequence of pp-definable subgroups, the…
Equivalents of NOTOP
Michael C. Laskowski, Danielle S. Ulrich
Working within the context of countable, superstable theories, we give many equivalents of a theory having NOTOP. In particular, NOTOP is equivalent to V-DI, the assertion that any…
Characterizing Borel Isomorphism Among Some Weakly Minimal Trivial Theories
Danielle Ulrich
We characterize having Borel isomorphism relation among some weakly minimal trivial theories, namely the examples of families of finite equivalence relations from recent joint work…
Borel complexity of families of finite equivalence relations via large cardinals
Michael C. Laskowski, Danielle S. Ulrich
We consider a large family of theories of equivalence relations, each with finitely many classes, and assuming the existence of an -Erdos cardinal, we determine which of these…