Abstract:

Vaught's conjecture states that any first order countable theory has
either countably many or continuum many countable models up to
isomorphism. In this paper Vaught's conjecture is proved for any theory
in the language of one unary operation. Also nn example is given of a
PC(L_{omega_1,omega}) sentence in one unary operation with exactly
omega_1 nonisomorphic countable models,

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