28 citations · 31 across the 9 of their papers we have counts for
16 papers
Classification Theory and the Construction of PAC Fields
Nicholas Ramsey
We analyze a construction of Cherlin, van den Dries, and Macintyre to code graphs in PAC fields. We show that, in many cases, model-theoretic properties of the graph are preserved…
A New Kim's Lemma
Alex Kruckman, Nicholas Ramsey
Kim's Lemma is a key ingredient in the theory of forking independence in simple theories. It asserts that if a formula divides, then it divides along every Morley sequence in type…
Generic Stability Independence and Treeless theories
Itay Kaplan, Nicholas Ramsey, Pierre Simon
We initiate a systematic study of \emph{generic stability independence} and introduce the class of \emph{treeless theories} in which this notion of independence is particularly wel…
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…
Invariant measures in simple and in small theories
Artem Chernikov, Ehud Hrushovski, Alex Kruckman +4
We give examples of (i) a simple theory with a formula (with parameters) which does not fork over the empty set but has mu measure 0 for every automorphism invariant Keisler measur…
Exact saturation in pseudo-elementary classes for simple and stable theories
Itay Kaplan, Nicholas Ramsey, Saharon Shelah
We study PC-exact saturation for stable and simple theories. Among other results, we show that PC-exact saturation characterizes the stability cardinals of size at least continuum…
Transitivity, lowness, and ranks in NSOP theories
Artem Chernikov, Byunghan Kim, Nicholas Ramsey
We develop the theory of Kim-independence in the context of NSOP theories satsifying the existence axiom. We show that, in such theories, Kim-independence is transitive and t…
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.
Local character of Kim-independence
Itay Kaplan, Nicholas Ramsey, Saharon Shelah
We show that NSOP theories are exactly the theories in which Kim-independence satisfies a form of local character. In particular, we show that if is NSOP, $M\models…
Generic expansion and Skolemization in NSOP theories
Alex Kruckman, Nicholas Ramsey
We study expansions of NSOP theories that preserve NSOP. We prove that if is a model complete NSOP theory eliminating the quantifier , then the ge…
On Kim-Independence
Itay Kaplan, Nicholas Ramsey
We study NSOP theories. We define Kim-independence, which generalizes non-forking independence in simple theories and corresponds to non-forking at a generic scale. We show t…
Invariants Related to the Tree Property
Nicholas Ramsey
We consider global analogues of model-theoretic tree properties. The main objects of study are the invariants related to Shelah's tree property , $κ_{\text{sct}}…
On model-theoretic tree properties
Artem Chernikov, Nicholas Ramsey
We study model theoretic tree properties () and their associated cardinal invariants (, respect…