8 found
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  1.  2
    Expansions of o-Minimal Structures by Dense Independent Sets.Alfred Dolich, Chris Miller & Charles Steinhorn - 2016 - Annals of Pure and Applied Logic 167 (8):684-706.
  2.  12
    Dp-Minimality: Basic Facts and Examples.Alfred Dolich, John Goodrick & David Lippel - 2011 - Notre Dame Journal of Formal Logic 52 (3):267-288.
    We study the notion of dp-minimality, beginning by providing several essential facts about dp-minimality, establishing several equivalent definitions for dp-minimality, and comparing dp-minimality to other minimality notions. The majority of the rest of the paper is dedicated to examples. We establish via a simple proof that any weakly o-minimal theory is dp-minimal and then give an example of a weakly o-minimal group not obtained by adding traces of externally definable sets. Next we give an example of a divisible ordered Abelian (...)
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  3. Forking and Independence in o-Minimal Theories.Alfred Dolich - 2004 - Journal of Symbolic Logic 69 (1):215-240.
  4.  3
    Extensions of Ordered Theories by Generic Predicates.Alfred Dolich, Chris Miller & Charles Steinhorn - 2013 - Journal of Symbolic Logic 78 (2):369-387.
  5.  17
    Model Completeness for Trivial, Uncountably Categorical Theories of Morley Rank 1.Alfred Dolich, Michael C. Laskowski & Alexander Raichev - 2006 - Archive for Mathematical Logic 45 (8):931-945.
    We show that if T is a trivial uncountably categorical theory of Morley Rank 1 then T is model complete after naming constants for a model.
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  6.  15
    A Note on Weakly O-Minimal Structures and Definable Completeness.Alfred Dolich - 2007 - Notre Dame Journal of Formal Logic 48 (2):281-292.
    We consider the extent to which certain properties of definably complete structures may persist in structures which are not definably complete, particularly in the weakly o-minimal structures.
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  7.  2
    Weak Dividing, Chain Conditions, and Simplicity.Alfred Dolich - 2003 - Archive for Mathematical Logic 43 (2):265-283.
    We study the properties of the independence relation given by weak dividing in simple theories. We also analyze abstract independence notions satisfying various axioms and relate these to the simple case.
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  8. A Note on Definable Completeness and Weak o-Minimality.Alfred Dolich - 2007 - Notre Dame Journal of Formal Logic 48:281-292.