First-order formulae are concise in acylindrically hyperbolic groups and other classes including Burnside, ICC, and torus knot groups, with results on finiteness of definable sets.
Sarkar,Commutators and squares in free groups, Algebr
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Concise formulae in groups of non-positive curvature
First-order formulae are concise in acylindrically hyperbolic groups and other classes including Burnside, ICC, and torus knot groups, with results on finiteness of definable sets.