Binary Simple Homogeneous Structures Are Supersimple with Finite Rank
نویسنده
چکیده
Suppose thatM is an in nite structure with nite relational vocabulary such that every relation symbol has arity at most 2. IfM is simple and homogeneous then its complete theory is supersimple with nite SU-rank which cannot exceed the number of complete 2-types over the empty set.
منابع مشابه
Supersimple 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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