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Additivity of the dprank
"... The main result is the prove of the linearity of the dprank. We also prove that the study of theories of finite dprank cannot be reduced to the study of its dpminimal types and discuss the possible relations between dprank and VCdensity. ..."
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The main result is the prove of the linearity of the dprank. We also prove that the study of theories of finite dprank cannot be reduced to the study of its dpminimal types and discuss the possible relations between dprank and VCdensity.
AN INDEPENDENCE THEOREM FOR NTP2 THEORIES
"... Abstract. We establish several results regarding dividing and forking in NTP2 theories. We show that dividing is the same as arraydividing. Combining it with existence of strictly invariant sequences we deduce that forking satisfies the chain condition over extension bases (namely, the forking idea ..."
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Abstract. We establish several results regarding dividing and forking in NTP2 theories. We show that dividing is the same as arraydividing. 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. hal00713494, version 2 13 Aug 2013
DENSE CODENSE PREDICATES AND NTP2
"... Abstract. We show that if T is any geometric theory having NTP2 then the corresponding theories of lovely pairs of models of T and of Hstructures associated to T also have NTP2. We also prove that if T is strong then the same two expansions of T are also strong. 1. ..."
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Abstract. We show that if T is any geometric theory having NTP2 then the corresponding theories of lovely pairs of models of T and of Hstructures associated to T also have NTP2. We also prove that if T is strong then the same two expansions of T are also strong. 1.