Abstract
S. Ulam asked about the number of non-isomorphic projective algebras withk generators. This paper answers his question for projective algebras of finite dimension at least three and shows that there are the maximum possible number, continuum many, of non-isomorphic one-generated structures of finite dimensionn, wheren is at least three, of the following kinds: projective set algebras, projective algebras, diagonal-free cylindric set algebras, diagonal-free cylindric algebras, and cylindric algebras.
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