5 papers
Measures on perfect e-free PAC fields
Zoé Chatzidakis, Nicholas Ramsey
We construct measures on definable sets in -free perfect PAC fields, as well as on perfect PAC fields whose absolute Galois groups are free pro- of finite rank. We deduce the…
Criteria for exact saturation and singular compactness
Itay Kaplan, Nicholas Ramsey, Saharon Shelah
We introduce the class of unshreddable theories, which contains the simple and NIP theories, and prove that such theories have exactly saturated models in singular cardinals, satis…
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…
Transitivity of Kim-independence
Itay Kaplan, Nicholas Ramsey
We prove several results on the behavior of Kim-independence upon changing the base in NSOP theories. As a consequence, we prove that Kim-independence satisfies transitivity…
A note on NSOP in one variable
Nicholas Ramsey
We prove that, in order to establish that a theory is NSOP, it suffices to show that no formula in a single free variable has SOP.