Some model theory of ${\rm SL}(2,{\mathbb R})$
Volume 229 / 2015
Fundamenta Mathematicae 229 (2015), 117-128
MSC: Primary 03C45, 03C64; Secondary 37B99.
DOI: 10.4064/fm229-2-2
Abstract
We study the action of $G = {\rm SL} (2,\mathbb R)$, viewed as a group definable in the structure $M = (\mathbb R,+,\times )$, on its type space $S_{G}(M)$. We identify a minimal closed $G$-flow $I$ and an idempotent $r\in I$ (with respect to the Ellis semigroup structure $*$ on $S_{G}(M)$). We also show that the “Ellis group” $(r*I,*)$ is nontrivial, in fact it is the group with two elements, yielding a negative answer to a question of Newelski.
