15 found
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  1.  16
    Non-Closure of the Image Model and Absence of Fixed Points.Claude Sureson - 1985 - Annals of Pure and Applied Logic 28 (3):287-314.
  2.  20
    A Generalization of von Neumann Regularity.Claude Sureson - 2005 - Annals of Pure and Applied Logic 135 (1-3):210-242.
    We propose two theories, one generalizing the notion of regularity, the other symmetric to it. Under two additional axioms one obtains model completeness of both theories. Models of these theories can be viewed as rings of sections of sheaves whose stalks are valuation rings. Regular rings correspond to the special case where all stalks are trivial valuation rings, that is fields.
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  3.  9
    Chang's Model and Covering Properties.Claude Sureson - 1989 - Annals of Pure and Applied Logic 42 (1):45-79.
  4. Π11‐Martin‐Löf Randomness and Π11‐Solovay Completeness.Claude Sureson - 2019 - Mathematical Logic Quarterly 65 (3):265-279.
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  5. Theory of Sets or Set of Theories?Claude Sureson - 1999 - Revue d'Histoire des Sciences 52 (1):107-138.
     
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  6.  13
    Théorie des Ensembles Ou Ensemble de Théories?/The Theory of Sets or Set of Theories?Claude Sureson - 1999 - Revue d'Histoire des Sciences 52 (1):107-138.
  7.  12
    Symmetric Submodels of a Cohen Generic Extension.Claude Sureson - 1992 - Annals of Pure and Applied Logic 58 (3):247-261.
    Sureson, C., Symmetric submodels of a Cohen generic extension, Annals of Pure and Applied Logic 58 247–261. We study some symmetric submodels of a Cohen generic extension and the satisfaction of several properties ) which strongly violate the axiom of choice.
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  8.  10
    Model Companion and Model Completion of Theories of Rings.Claude Sureson - 2009 - Archive for Mathematical Logic 48 (5):403-420.
    Extending the language of rings to include predicates for Jacobson radical relations, we show that the theory of regular rings defined by Carson, Lipshitz and Saracino is the model completion of the theory of semisimple rings. Removing the requirement on the Jacobson radical (reduced to {0}), we prove that the theory of rings with no nilpotents does not admit a model companion relative to this augmented language.
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  9.  7
    A Valuation Ring Analogue of von Neumann Regularity.Claude Sureson - 2007 - Annals of Pure and Applied Logic 145 (2):204-222.
    We continue the study of a theory which is a valued analogue of the theory of regular rings studied by Carson, Lipshitz and Saracino, characterize it as the model companion of the theory of Prüfer rings, and prove its decidability. We then link it to the theory of p.p. rings developed by Weispfenning and show that it admits quantifier elimination in a related language.
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  10.  9
    Rumely Domains with Atomic Constructible Boolean Algebra. An Effective Viewpoint.Claude Sureson - 2007 - Notre Dame Journal of Formal Logic 48 (3):399-423.
    The archetypal Rumely domain is the ring \widetildeZ of algebraic integers. Its constructible Boolean algebra is atomless. We study here the opposite situation: Rumely domains whose constructible Boolean algebra is atomic. Recursive models (which are rings of algebraic numbers) are proposed; effective model-completeness and decidability of the corresponding theory are proved.
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  11.  18
    About Prikry Generic Extensions.Claude Sureson - 1991 - Annals of Pure and Applied Logic 51 (3):247-278.
  12.  17
    The Model< I> N=∪{< I> L_[A]:< I> A Countable Set of Ordinals}.Claude Sureson - 1987 - Annals of Pure and Applied Logic 36:289-313.
  13.  14
    The Model N = ∪ {L[A]: A Countable Set of Ordinals}.Claude Sureson - 1987 - Annals of Pure and Applied Logic 36:289-313.
    This paper continues the study of covering properties of models closed under countable sequences. In a previous article we focused on C. Chang's Model . Our purpose is now to deal with the model N = ∪ { L [A]: A countable ⊂ Ord}. We study here relations between covering properties, satisfaction of ZF by N , and cardinality of power sets. Under large cardinal assumptions N is strictly included in Chang's Model C , it may thus be interesting to (...)
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  14.  7
    Complexity of Κ-Ultrafilters and Inner Models with Measurable Cardinals.Claude Sureson - 1984 - Journal of Symbolic Logic 49 (3):833-841.
  15.  19
    Omega ¹-Constructible Universe and Measurable Cardinals.Claude Sureson - 1986 - Annals of Pure and Applied Logic 30 (3):293.