First-order rigidity of rings satisfying polynomial identities

First order rigidity of homeomorphism groups of manifolds

“…We remark that Theorem 1.3 fits within a tradition of results proving first order rigidity of various structures, such as lattices in higher rank [2], function fields [11,12,38,32], rings [24,17], finite-by-abelian groups [28], and linear groups [31], and into the philosophy of distinguishing between objects that are difficult to access directly via finite syntactic objects.…”