Author:
YAACOV ITAÏ BEN,CHERNIKOV ARTEM
Abstract
Abstract
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.
Publisher
Cambridge University Press (CUP)
Cited by
11 articles.
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