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Miklos Schweitzer 1968_6

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October 8, 2008
superior algebrasuperior algebra unsolved

Problem Statement

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