Some model theory of SL(2,R)

TL;DR

This paper investigates the model-theoretic properties of SL(2,R) acting on its type space, identifying a minimal flow and an idempotent, and revealing a two-element group structure that answers a prior open question.

Contribution

It provides a detailed analysis of the type space of SL(2,R), identifying a minimal flow and an idempotent, and demonstrates a specific two-element group structure, addressing a question in model theory.

Findings

Identified a minimal closed G-flow I.

Found an idempotent r in I with respect to the Ellis semigroup.

Showed that (r*I,*) has exactly 2 elements.

Abstract

We study the action of G = SL(2,R) on its type space S_G(R) where R denotes the field of real numbers. We identify a minimal closed G-flow I, and an idempotent r of I (with the respect to the Ellis semigroup structure * on I). We show that the group (r*I,*) has 2 elements, yielding a negative answer to a question of Newelski.