Notre Dame Journal of Formal Logic

Semigroups in Stable Structures

Yatir Halevi

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Assume that G is a definable group in a stable structure M. Newelski showed that the semigroup SG(M) of complete types concentrated on G is an inverse limit of the -definable (in Meq) semigroups SG,Δ(M). He also showed that it is strongly π-regular: for every pSG,Δ(M), there exists nN such that pn is in a subgroup of SG,Δ(M). We show that SG,Δ(M) is in fact an intersection of definable semigroups, so SG(M) is an inverse limit of definable semigroups, and that the latter property is enjoyed by all -definable semigroups in stable structures.

Article information

Notre Dame J. Formal Logic, Volume 59, Number 3 (2018), 417-436.

Received: 16 September 2015
Accepted: 9 May 2016
First available in Project Euclid: 20 June 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03C60: Model-theoretic algebra [See also 08C10, 12Lxx, 13L05] 03C98: Applications of model theory [See also 03C60]
Secondary: 03C45: Classification theory, stability and related concepts [See also 03C48]

stable groups stable semigroups strong pi-regularity epigroup Newelski’s semigroup


Halevi, Yatir. Semigroups in Stable Structures. Notre Dame J. Formal Logic 59 (2018), no. 3, 417--436. doi:10.1215/00294527-2018-0003.

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