Nice Enumerations of Ω-categorical Groups
نویسنده
چکیده
We give an example of an ω-categorical group without AZ-enumerations. We build AZ-enumerations of some ω-categorical central products of ω copies of a finite 2-step nilpotent group.
منابع مشابه
An ℵ0-categorical theory which is not G-compact and does not have AZ-enumerations
3 4 We give an example of an א0-categorical theory which is not G-compact. The countable model of this theory does not have AZ-enumerations.
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In two recent papers with Krzysztof Krupi´nski, we proved that every ω-categorical, generically stable group is nilpotent-by-finite and that every ω-categorical, generically stable ring is nilpotent-by-finite. During the lecture, after a brief overview of well-known results on ω-categorical groups and rings, I will explain the main ideas of the proofs of our results.
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متن کاملSupersimple Ω-categorical Groups and Theories
An ω-categorical supersimple group is finite-by-abelian-by-finite, and has finite SU -rank. Every definable subgroup is commensurable with an acl(∅)definable subgroup. Every finitely based regular type in a CM-trivial ω-categorical simple theory is non-orthogonal to a type of SU -rank 1. In particular, a supersimple ω-categorical CM-trivial theory has finite SU -rank.
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تاریخ انتشار 2006