Stability in a group (Q2076074)

Summary: We develop local stable group theory directly from topological dynamics, and extend the main tools in this subject to the setting of stability ``in a model.'' Specifically, given a group \(G\), we analyze the structure of sets \(A \subseteq G\) such that the bipartite relation \(xy\in A\) omits infinite half-graphs. Our proofs rely on the characterization of model-theoretic stability via Grothendieck's ``double-limit'' theorem (as shown by \textit{I. Ben Yaacov} [Bull. Symb. Log. 20, No. 4, 491--496 (2014; Zbl 1345.03058)]), and the work of \textit{R. Ellis} and \textit{M. Nerurkar} [Trans. Am. Math. Soc. 313, No. 1, 103--119 (1989; Zbl 0674.54026)] on weakly almost periodic \(G\)-flows.