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2018 Semigroups in Stable Structures
Yatir Halevi
Notre Dame J. Formal Logic 59(3): 417-436 (2018). DOI: 10.1215/00294527-2018-0003


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.


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Yatir Halevi. "Semigroups in Stable Structures." Notre Dame J. Formal Logic 59 (3) 417 - 436, 2018.


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

zbMATH: 06939329
MathSciNet: MR3832090
Digital Object Identifier: 10.1215/00294527-2018-0003

Primary: 03C60 , 03C98
Secondary: 03C45

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

Rights: Copyright © 2018 University of Notre Dame


Vol.59 • No. 3 • 2018
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