Notre Dame Journal of Formal Logic

Semigroups in Stable Structures

Yatir Halevi

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1529481617

Digital Object Identifier
doi:10.1215/00294527-2018-0003

Mathematical Reviews number (MathSciNet)
MR3832090

Zentralblatt MATH identifier
06939329

Subjects
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]

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

Citation

Halevi, Yatir. Semigroups in Stable Structures. Notre Dame J. Formal Logic 59 (2018), no. 3, 417--436. doi:10.1215/00294527-2018-0003. https://projecteuclid.org/euclid.ndjfl/1529481617


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