Semigroups in Stable Structures
| Autor: | Yatir Halevi |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
stable semigroups
Pure mathematics Newelski’s semigroup Mathematics::Operator Algebras Logic Group (mathematics) Semigroup epigroup 010102 general mathematics Structure (category theory) stable groups Mathematics - Logic 0102 computer and information sciences 01 natural sciences 03C45 010201 computation theory & mathematics FOS: Mathematics strong pi-regularity Epigroup Inverse limit 03C60 0101 mathematics Logic (math.LO) 03C98 Mathematics |
| Zdroj: | Notre Dame J. Formal Logic 59, no. 3 (2018), 417-436 |
| ISSN: | 0029-4527 |
| DOI: | 10.1215/00294527-2018-0003 |
| Popis: | Assume that $G$ is a definable group in a stable structure $M$ . Newelski showed that the semigroup $S_{G}(M)$ of complete types concentrated on $G$ is an inverse limit of the $\infty$ -definable (in $M^{\mathrm{eq}}$ ) semigroups $S_{G,\Delta}(M)$ . He also showed that it is strongly $\pi$ -regular: for every $p\inS_{G,\Delta}(M)$ , there exists $n\in\mathbb{N}$ such that $p^{n}$ is in a subgroup of $S_{G,\Delta}(M)$ . We show that $S_{G,\Delta}(M)$ is in fact an intersection of definable semigroups, so $S_{G}(M)$ is an inverse limit of definable semigroups, and that the latter property is enjoyed by all $\infty$ -definable semigroups in stable structures. |
| Databáze: | OpenAIRE |
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