3 papers
math.LO2021
On rank not only in NSOP1 theories
Jan Dobrowolski, Daniel Max Hoffmann
We introduce a family of local ranks DQ depending on a finite set Q of pairs of the form (φ(x,y),q(y)) where φ(x,y) is a formula and q(y) is a global type. We prove that in any NSO…
math.LO2019
Independence over arbitrary sets in NSOP theories
Jan Dobrowolski, Byunghan Kim, Nicholas Ramsey
We study Kim-independence over arbitrary sets. Assuming that forking satisfies existence, we establish Kim's lemma for Kim-dividing over arbitrary sets in an NSOP theory. We…
math.LO2018
On omega-categorical groups and rings of finite burden
Frank Olaf Wagner, Jan Dobrowolski
An -categorical group of finite burden is virtually finite-by-abelian; an -categorical ring of finite burden is virtually finite-by-null; an -categorical NTP2 ring is virt…