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The Journal of Symbolic Logic The Journal of Symbolic Logic

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Isomorphic but not lower base-isomorphic cylindric set algebras

Published online by Cambridge University Press:  12 March 2014

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

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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 53 , Issue 3 , September 1988 , pp. 846 - 853
Copyright
Copyright © Association for Symbolic Logic 1988

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References

[AN 81]Andréka, H. and Németi, I., Oncylindric-relativized set algebras, [HMTAN 81], pp. 131–315.Google Scholar
[B 85]Biró, B., Isomorphic but not base-isomorphic base-minimal cylindric algebras, Algebra Universalis (to appear).Google Scholar
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[B 87]Biró, B., Isomorphism does not imply base-isomorphism for cylindric algebras that are not locally finite or not regular, Commentationes Mathematicae Universitatis Carolinae, vol. 28 (1987), pp. 221–226.Google Scholar
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[HMT 85]Henkin, L., Cylindric algebras. Part II, North-Holland, Amsterdam.Google Scholar
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