Low rank MSO, a restriction of MSO to bounded-cutrank set quantification, is expressively equivalent to flip-reachability logic on all undirected graphs, to separator logic on weakly sparse classes, and to flip-connectivity logic on bounded-VC-dimension classes.
Indiscernibles and flatness in monadically stable and monadically NIP classes
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Low rank MSO
Low rank MSO, a restriction of MSO to bounded-cutrank set quantification, is expressively equivalent to flip-reachability logic on all undirected graphs, to separator logic on weakly sparse classes, and to flip-connectivity logic on bounded-VC-dimension classes.