Isomorphic but not lower base-isomorphic cylindric set algebras

Abstract

AbstractThis paper belongs to cylindric-algebraic model theory understood in the sense of algebraic logic. We show the existence of isomorphic but not lower base-isomorphic cylindric set algebras. These algebras are regular and locally finite. This solves a problem raised in [N 83] which was implicitly present also in [HMTAN 81]. This result implies that a theorem of Vaught for prime models of countable languages does not continue to hold for languages of any greater power.