Definability properties and the congruence closure

We introduce a natural class of quantifiers Th containing all monadic type quantifiers, all quantifiers for linear orders, quantifiers for isomorphism, Ramsey type quantifiers, and plenty more, showing that no sublogic of Lo~o,(Th) or countably compact regular sublogic of L~o,(Th), properly extending L,o,o, satisfies the uniform reduction property for quotients. As a consequence, none of these logics satisfies either A-interpolation or Beth's definability theorem when closed under relativizations. We also show the failure of both properties for any sublogic of L~o~(Th) in which Chang's quantifier or some cardinality quantifier Q,, with > 1, is definable.