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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 definable Galois groups and the strong canonical base property.Daniel Palacín & Anand Pillay - 2017 - Journal of Mathematical Logic 17 (1):1750002.
    In [E. Hrushovski, D. Palacín and A. Pillay, On the canonical base property, Selecta Math. 19 865–877], Hrushovski and the authors proved, in a certain finite rank environment, that rigidity of definable Galois groups implies that [Formula: see text] has the canonical base property in a strong form; “internality to” being replaced by “algebraicity in”. In the current paper, we give a reasonably robust definition of the “strong canonical base property” in a rather more general finite rank context than [E. (...)
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  • Elimination of Hyperimaginaries and Stable Independence in Simple CM-Trivial Theories.D. Palacín & F. O. Wagner - 2013 - Notre Dame Journal of Formal Logic 54 (3-4):541-551.
    In a simple CM-trivial theory every hyperimaginary is interbounded with a sequence of finitary hyperimaginaries. Moreover, such a theory eliminates hyperimaginaries whenever it eliminates finitary hyperimaginaries. In a supersimple CM-trivial theory, the independence relation is stable.
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  • Additive Covers and the Canonical Base Property.Michael Loesch - 2023 - Journal of Symbolic Logic 88 (1):118-144.
    We give a new approach to the failure of the Canonical Base Property (CBP) in the so far only known counterexample, produced by Hrushovski, Palacín and Pillay. For this purpose, we will give an alternative presentation of the counterexample as an additive cover of an algebraically closed field. We isolate two fundamental weakenings of the CBP, which already appeared in work of Chatzidakis and Moosa-Pillay and show that they do not hold in the counterexample. In order to do so, a (...)
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  • Unimodularity unified.Darío García & Frank O. Wagner - 2017 - Journal of Symbolic Logic 82 (3):1051-1065.
    Unimodularity is localized to a complete stationary type, and its properties are analysed. Some variants of unimodularity for definable and type-definable sets are introduced, and the relationship between these different notions is studied. In particular, it is shown that all notions coincide for non-multidimensional theories where the dimensions are associated to strongly minimal types.
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