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Isomorphic but not lower base-isomorphic cylindric set algebras

Published online by Cambridge University Press:  12 March 2014

B. Biró
Mathematical Institute, Hungarian Academy of Sciences, H-1364 Budapest, Hungary
S. Shelah
Institute of Mathematics, The Hebrew University, Jerusalem, Israel


This 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.

Research Article
Copyright © Association for Symbolic Logic 1988

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