On minimal flows. definably amenable groups, and o-minimality

2015/04/03 by Anand Pillay, Pillay, Anand, Ningyuan Yao +1
Computer Science · Mathematics · #03C64 #54H20 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO) #math.DS #math.GR #math.LO #msc:03C64 #msc:54H20 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1504.00875

23 pages

arxiv created 2015/04/03 · openalex publication_date 2015/04/03 · arxiv updated 2015/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study definably amenable groups in NIP theories, and answer a question of Newelski (and also of Chernikov-Simon), by giving an example in the o-minimal context where weak generic types do not coincide with almost periodic types, equivalently where the union of the minimal subflows of suitable type spaces is not closed. We give other positive results in this o-minimal context.

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