Browsing by Autor "Assaf Hasson"
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Item type: Item , Definable one dimensional structures in o-minimal theories(Hebrew University of Jerusalem, 2010) Assaf Hasson; Alf Onshuus; Ya’acov PeterzilItem type: Item , Definable structures in o-minimal theories: One dimensional types(Hebrew University of Jerusalem, 2010) Assaf Hasson; Alf Onshuus; Ya’acov PeterzilItem type: Item , Stable types in rosy theories(Cambridge University Press, 2010) Assaf Hasson; Alf OnshuusAbstract We study the behaviour of stable types in rosy theories. The main technical result is that a non-þ-forking extension of an unstable type is unstable. We apply this to show that a rosy group with a þ-generic stable type is stable. In the context of super-rosy theories of finite rank we conclude that non-trivial stable types of U þ -rank 1 must arise from definable stable sets.Item type: Item , Unstable structures definable in o-minimal theories(Cornell University, 2007) Assaf Hasson; Alf OnshuusLet M be an o-minimal structure with elimination of imaginaries, N an unstable structure definable in M. Then there exists X, interpretable in N, such that X with all the structure induced from N is o-minimal. In particular X is linearly ordered. As part of the proof we show: Theorem 1: If the M-dimenson of N is 1 then any 1-N-type is either strongly stable or finite by o-minimal. Theorem 2: If N is N-minimal then it is 1-M-dimensional.Item type: Item , Unstable structures definable in o-minimal theories(Birkhäuser, 2010) Assaf Hasson; Alf Onshuus