Let \Psi\equal{}\langle A;...\rangle be an arbitrary, countable algebraic structure (that is, Ψ can have an arbitrary number of finitary operations and relations). Prove that Ψ has as many as continuum automorphisms if and only if for any finite subset A′ of A there is an automorphism πA′ of Ψ different from the identity automorphism and such that (x) \pi_{A'}\equal{}x for every x∈A′.
M. Makkai superior algebrasuperior algebra unsolved