4 papers
Existential characterizations of monadic NIP
Samuel Braunfeld, Michael C. Laskowski
We show that if a universal theory is not monadically NIP, then this is witnessed by a canonical configuration defined by an existential formula. As a consequence, we show that a h…
Indiscernibles in monadically NIP theories
Samuel Braunfeld, Michael C. Laskowski
We prove various results around indiscernibles in monadically NIP theories. First, we provide several characterizations of monadic NIP in terms of indiscernibles, mirroring previou…
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…
An analogue of U-rank for atomic classes
John T. Baldwin, Michael C. Laskowski, Saharon Shelah
For a countable, complete, first-order theory , we study , the class of atomic models of . We develop an analogue of -rank and prove two results. On one hand, if some…