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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
[B 86]Biró, B., Lower base-isomorphisms of relation algebras and cylindric algebras, manuscript, Mathematical Institute of the Hungarian Academy of Sciences, Budapest.Google Scholar
[B 86a]Biró, B., Isomorphic but not lower base-isomorphic cylindric algebras of finite dimension, Notre Dame Journal of Formal Logic (to appear).Google Scholar
[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
[ChK 73]Chang, C. C. and Keisler, H. J., Model theory, North-Holland, Amsterdam.Google Scholar
[HMT 71]Henkin, L., Monk, J. D. and Tarski, A., Cylindric algebras. Part I, North-Holland, Amsterdam.Google Scholar
[HMT 81]Henkin, L., Cylindric set algebras and related structures, [HMTAN 81], pp. 1–129.Google Scholar
[HMT 85]Henkin, L., Cylindric algebras. Part II, North-Holland, Amsterdam.Google Scholar
[HMTAN 81]Henkin, L., Monk, J. D., Tarski, A., Andréka, H. and Németi, I., Cylindric set algebras, Lecture Notes in Mathematics, vol. 883, Springer-Verlag, Berlin.Google Scholar
[L 85]Larson, J., The number of one-generated cylindric set algebras of dimension greater than two, this Journal, vol. 50, pp. 59–71.Google Scholar
[M 76]Monk, J. D., Mathematical logic, Springer-Verlag, Berlin.CrossRefGoogle Scholar
[N 83]Németi, I., Cylindric relativised set algebras and Boolean algebras with operators have SAP; which lead lo notes on algebraic model theory. Preprint No. 1983/4, Mathematical Institute of the Hungarian Academy of Sciences, Budapest.Google Scholar
[S 83]Serény, G., On regular locally finite-dimensional cylindric set algebras with atomic neat reducts, preprint, Polytechnical University of Budapest.Google Scholar
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