Vaught's conjecture for theories of one unary operation, Fundamenta Mathematicae, 111(1981), 135-141.

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,

electronic copy from