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Existentially closed algebras and boolean products

Published online by Cambridge University Press:  12 March 2014

Herbert H. J. Riedel
Herbert H. J. Riedel*
Affiliation:
The Citadel, Charleston, South Carolina 29409
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Abstract

A Boolean product construction is used to give examples of existentially closed algebras in the universal Horn class ISP(K) generated by a universal class K of finitely subdirectly irreducible algebras such that Γa(K) has the Fraser-Horn property. If ⟦a ≠ b⟧ ∩ ⟦c ≠ d ⟧ = ∅ is definable in K and K has a model companion of K-simple algebras, then it is shown that ISP(K) has a model companion. Conversely, a sufficient condition is given for ISP(K) to have no model companion.

Keywords

Existentially closedBoolean productssheavesmodel companionuniversal Horn classFraser-Horn property.
Type
Survey/expository papers
Information
The Journal of Symbolic Logic , Volume 53 , Issue 2 , June 1988 , pp. 571 - 596
Copyright
Copyright © Association for Symbolic Logic 1988

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Footnotes

1

The results presented in this paper form a part of the author's Ph.D. thesis, completed at the University of Waterloo in 1984 under Professor Stanley Burris, whose supervision and assistance is gratefully acknowledged.

References

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