Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 59, Number 3 (2018), 417-436.
Semigroups in Stable Structures
Assume that is a definable group in a stable structure . Newelski showed that the semigroup of complete types concentrated on is an inverse limit of the -definable (in ) semigroups . He also showed that it is strongly -regular: for every , there exists such that is in a subgroup of . We show that is in fact an intersection of definable semigroups, so is an inverse limit of definable semigroups, and that the latter property is enjoyed by all -definable semigroups in stable structures.
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
Permanent link to this document
Digital Object Identifier
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]
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