2,732 research outputs found
An independence theorem for NTP2 theories
We establish several results regarding dividing and forking in NTP2 theories.
We show that dividing is the same as array-dividing. Combining it with
existence of strictly invariant sequences we deduce that forking satisfies the
chain condition over extension bases (namely, the forking ideal is S1, in
Hrushovski's terminology). Using it we prove an independence theorem over
extension bases (which, in the case of simple theories, specializes to the
ordinary independence theorem). As an application we show that Lascar strong
type and compact strong type coincide over extension bases in an NTP2 theory.
We also define the dividing order of a theory -- a generalization of Poizat's
fundamental order from stable theories -- and give some equivalent
characterizations under the assumption of NTP2. The last section is devoted to
a refinement of the class of strong theories and its place in the
classification hierarchy
Independence Logic and Abstract Independence Relations
We continue the work on the relations between independence logic and the
model-theoretic analysis of independence, generalizing the results of [15] and
[16] to the framework of abstract independence relations for an arbitrary AEC.
We give a model-theoretic interpretation of the independence atom and
characterize under which conditions we can prove a completeness result with
respect to the deductive system that axiomatizes independence in team semantics
and statistics
Amalgamation of types in pseudo-algebraically closed fields and applications
This paper studies unbounded PAC fields and shows an amalgamation result for
types over algebraically closed sets. It discusses various applications, for
instance that omega-free PAC fields have the property NSOP3. It also contains a
description of imaginaries in PAC fields.Comment: Minor changes in v3. Accepted versio
- …