10 found
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  1.  16
    Characterizing Rosy Theories.Clifton Ealy & Alf Onshuus - 2007 - Journal of Symbolic Logic 72 (3):919 - 940.
    We examine several conditions, either the existence of a rank or a particular property of þ-forking that suggest the existence of a well-behaved independence relation, and determine the consequences of each of these conditions towards the rosiness of the theory. In particular we show that the existence of an ordinal valued equivalence relation rank is a (necessary and) sufficient condition for rosiness.
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  2.  22
    Properties and Consequences of Thorn-Independence.Alf Onshuus - 2006 - Journal of Symbolic Logic 71 (1):1 - 21.
    We develop a new notion of independence (þ-independence, read "thorn"-independence) that arises from a family of ranks suggested by Scanlon (þ-ranks). We prove that in a large class of theories (including simple theories and o-minimal theories) this notion has many of the properties needed for an adequate geometric structure. We prove that þ-independence agrees with the usual independence notions in stable, supersimple and o-minimal theories. Furthermore, we give some evidence that the equivalence between forking and þ-forking in simple theories might (...)
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  3.  13
    On Dp-Minimality, Strong Dependence and Weight.Alf Onshuus & Alexander Usvyatsov - 2011 - Journal of Symbolic Logic 76 (3):737 - 758.
    We study dp-minimal and strongly dependent theories and investigate connections between these notions and weight.
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  4.  13
    The Independence Property in Generalized Dense Pairs of Structures.Alexander Berenstein, Alf Dolich & Alf Onshuus - 2011 - Journal of Symbolic Logic 76 (2):391 - 404.
    We provide a general theorem implying that for a (strongly) dependent theory T the theory of sufficiently well-behaved pairs of models of T is again (strongly) dependent. We apply the theorem to the case of lovely pairs of thorn-rank one theories as well as to a setting of dense pairs of first-order topological theories.
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  5.  19
    Stable Domination and Weight.Alf Onshuus & Alexander Usvyatsov - 2011 - Annals of Pure and Applied Logic 162 (7):544-560.
    We develop the theory of domination by stable types and stable weight in an arbitrary theory.
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  6.  16
    Stable Types in Rosy Theories.Assaf Hasson & Alf Onshuus - 2010 - Journal of Symbolic Logic 75 (4):1211-1230.
    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.
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  7.  14
    On Linearly Ordered Structures of Finite Rank.Alf Onshuus & Charles Steinhorn - 2009 - Journal of Mathematical Logic 9 (2):201-239.
  8.  6
    A Note on Stable Sets, Groups, and Theories with NIP.Alf Onshuus & Ya'acov Peterzil - 2007 - Mathematical Logic Quarterly 53 (3):295-300.
    Let M be an arbitrary structure. Then we say that an M -formula φ defines a stable set inM if every formula φ ∧ α is stable. We prove: If G is an M -definable group and every definable stable subset of G has U -rank at most n , then G has a maximal connected stable normal subgroup H such that G /H is purely unstable. The assumptions hold for example if M is interpretable in an o-minimal structure.More generally, (...)
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  9.  14
    Classifying Torsion Free Groups in o-Minimal Expansions of Real Closed Fields.Eliana Barriga & Alf Onshuus - 2016 - Annals of Pure and Applied Logic 167 (12):1267-1297.
  10.  11
    Consistent Amalgamation for Þ-Forking.Clifton Ealy & Alf Onshuus - 2014 - Annals of Pure and Applied Logic 165 (2):503-519.
    In this paper, we prove the following:Theorem. Let M be a rosy dependent theory and letp,pbe non-þ-forking extensions ofp∈Switha0a1; assume thatp∪pis consistent and thata0,a1start a þ-independent indiscernible sequence. Thenp∪pis a non-þ-forking extension ofp.We also provide an example to show that the result is not true without assuming NIP.
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