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  1. Plus ultra.Frank O. Wagner - 2015 - Journal of Mathematical Logic 15 (2):1550008.
    We define a reasonably well-behaved class of ultraimaginaries, i.e. classes modulo [Formula: see text]-invariant equivalence relations, called tame, and establish some basic simplicity-theoretic facts. We also show feeble elimination of supersimple ultraimaginaries: If [Formula: see text] is an ultraimaginary definable over a tuple [Formula: see text] with [Formula: see text], then [Formula: see text] is eliminable up to rank [Formula: see text]. Finally, we prove some uniform versions of the weak canonical base property.
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  • On pseudolinearity and generic pairs.Evgueni Vassiliev - 2010 - Mathematical Logic Quarterly 56 (1):35-41.
    We continue the study of the connection between the “geometric” properties of SU -rank 1 structures and the properties of “generic” pairs of such structures, started in [8]. In particular, we show that the SU-rank of the theory of generic pairs of models of an SU -rank 1 theory T can only take values 1 , 2 or ω, generalizing the corresponding results for a strongly minimal T in [3]. We also use pairs to derive the implication from pseudolinearity to (...)
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  • Constructing the hyperdefinable group from the group configuration.Tristram de Piro, Byunghan Kim & Jessica Millar - 2006 - Journal of Mathematical Logic 6 (2):121-139.
    Under [Formula: see text]-amalgamation, we obtain the canonical hyperdefinable group from the group configuration.
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  • Un critère simple.Thomas Blossier & Amador Martin-Pizarro - 2019 - Notre Dame Journal of Formal Logic 60 (4):639-663.
    Nous isolons des propriétés valables dans certaines théories de purs corps ou de corps munis d’opérateurs afin de montrer qu’une théorie est simple lorsque les clôtures définissables et algébriques sont contrôlées par une théorie stable associée.
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  • Simple almost hyperdefinable groups.Itaï Ben-Yaacov - 2006 - Journal of Mathematical Logic 6 (01):69-88.
    We lay down the groundwork for the treatment of almost hyperdefinable groups: notions from [5] are put into a natural hierarchy, and new notions, essential to the study to such groups, fit elegantly into this hierarchy. We show that "classical" properties of definable and hyperdefinable groups in simple theories can be generalised to this context. In particular, we prove the existence of stabilisers of Lascar strong types and of the connected and locally connected components of subgroups, and that in a (...)
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  • Compactness and independence in non first order frameworks.Itay Ben-Yaacov - 2005 - Bulletin of Symbolic Logic 11 (1):28-50.
    This communication deals with positive model theory, a non first order model theoretic setting which preserves compactness at the cost of giving up negation. Positive model theory deals transparently with hyperimaginaries, and accommodates various analytic structures which defy direct first order treatment. We describe the development of simplicity theory in this setting, and an application to the lovely pairs of models of simple theories without the weak non finite cover property.
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