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Clifton Ealy [6]Clifton F. Ealy [1]
  1.  38
    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.  20
    Superrosy Dependent Groups Having Finitely Satisfiable Generics.Clifton Ealy, Krzysztof Krupiński & Anand Pillay - 2008 - Annals of Pure and Applied Logic 151 (1):1-21.
    We develop a basic theory of rosy groups and we study groups of small Uþ-rank satisfying NIP and having finitely satisfiable generics: Uþ-rank 1 implies that the group is abelian-by-finite, Uþ-rank 2 implies that the group is solvable-by-finite, Uþ-rank 2, and not being nilpotent-by-finite implies the existence of an interpretable algebraically closed field.
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  3.  13
    Thorn-Forking in Continuous Logic.Clifton Ealy & Isaac Goldbring - 2012 - Journal of Symbolic Logic 77 (1):63-93.
    We study thorn forking and rosiness in the context of continuous logic. We prove that the Urysohn sphere is rosy (with respect to finitary imaginaries), providing the first example of an essentially continuous unstable theory with a nice notion of independence. In the process, we show that a real rosy theory which has weak elimination of finitary imaginaries is rosy with respect to finitary imaginaries, a fact which is new even for discrete first-order real rosy theories.
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  4.  10
    Thorn Independence in the Field of Real Numbers with a Small Multiplicative Group.Alexander Berenstein, Clifton Ealy & Ayhan Günaydın - 2007 - Annals of Pure and Applied Logic 150 (1-3):1-18.
    We characterize þ-independence in a variety of structures, focusing on the field of real numbers expanded by predicate defining a dense multiplicative subgroup, G, satisfying the Mann property and whose pth powers are of finite index in G. We also show such structures are super-rosy and eliminate imaginaries up to codes for small sets.
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  5.  15
    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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  6.  12
    Model Completeness of o-Minimal Fields with Convex Valuations.Clifton F. Ealy & Jana Maříková - 2015 - Journal of Symbolic Logic 80 (1):234-250.
  7.  9
    Residue Field Domination in Real Closed Valued Fields.Clifton Ealy, Deirdre Haskell & Jana Maříková - 2019 - Notre Dame Journal of Formal Logic 60 (3):333-351.
    We define a notion of residue field domination for valued fields which generalizes stable domination in algebraically closed valued fields. We prove that a real closed valued field is dominated by the sorts internal to the residue field, over the value group, both in the pure field and in the geometric sorts. These results characterize forking and þ-forking in real closed valued fields. We lay some groundwork for extending these results to a power-bounded T-convex theory.
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