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Ample thoughts
Journal of Symbolic Logic 78 (2):489-510 (2013)
Abstract
Non-$n$-ampleness as defined by Pillay [20] and Evans [5] is preserved under analysability. Generalizing this to a more general notion of $\Sigma$-ampleness, this gives an immediate proof for all simple theories of a weakened version of the Canonical Base Property (CBP) proven by Chatzidakis [4] for types of finite SU-rank. This is then applied to the special case of groupsOther Versions
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Citations of this work
Rings of finite Morley rank without the canonical base property.Michael Loesch & Daniel Palacín - 2025 - Journal of Mathematical Logic 25 (2).
On definable Galois groups and the strong canonical base property.Daniel Palacín & Anand Pillay - 2017 - Journal of Mathematical Logic 17 (1):1750002.
Additive Covers and the Canonical Base Property.Michael Loesch - 2023 - Journal of Symbolic Logic 88 (1):118-144.
Domination, Fibrations, and Splitting.Christine Eagles & Léo Jimenez - forthcoming - Journal of Symbolic Logic:1-23.
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.
References found in this work
A new strongly minimal set.Ehud Hrushovski - 1993 - Annals of Pure and Applied Logic 62 (2):147-166.
The Manin–Mumford conjecture and the model theory of difference fields.Ehud Hrushovski - 2001 - Annals of Pure and Applied Logic 112 (1):43-115.
Vaught’s conjecture for superstable theories of finite rank.Steven Buechler - 2008 - Annals of Pure and Applied Logic 155 (3):135-172.
The geometry of forking and groups of finite Morley rank.Anand Pillay - 1995 - Journal of Symbolic Logic 60 (4):1251-1259.
A note on CM-Triviality and the geometry of forking.Anand Pillay - 2000 - Journal of Symbolic Logic 65 (1):474-480.
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