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Filtral powers of structures

Published online by Cambridge University Press:  12 March 2014

P. Ouwehand  and
H. Rose
P. Ouwehand
Affiliation:
Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7700, South Africa. E-mail: peter2@maths.uct.ac.za
H. Rose
Affiliation:
Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7700, South Africa. E-mail: rose@maths.uct.ac.za
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Abstract

Among the results of this paper are the following:

1. Every Boolean (ultra)power is the union of an updirected elementary family of direct ultrapowers.

2. Under certain conditions, a finitely iterated Boolean ultrapower is isomorphic to a single Boolean ultrapower.

3. A ω-bounded filtral power is an elementary substructure of a filtral power.

4. Let be an elementary class closed under updirected unions (e.g., if is an amalgamation class); then is closed under finite products if and only if is closed under reduced products if and only if is a Horn class.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 63 , Issue 4 , December 1998 , pp. 1239 - 1254
Copyright
Copyright © Association for Symbolic Logic 1998

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References

REFERENCES

[1] Ash, C. J., Reduced powers and Boolean extensions, Journal of the London Mathematical Society, vol. 9 (1975), pp. 429–432.Google Scholar
[2] Banaschewski, B. and Nelson, E., Elementary properties of limit reduced powers with applications to Boolean powers, Colloquia Mathematica Societatis János Bolyai, vol. ? (1975), pp. 21–24.Google Scholar
[3] Banaschewski, B. and Nelson, E., Boolean powers as algebras of continuous functions, Dissertationes Mathematica, no. 179, Warsaw, 1980.Google Scholar
[4] Bergman, C., The amalgamation class of a discriminator variety is finitely axiomatizable, Universal algebra and lattice theory, proceedings, puebla 1982, Lecture Notes in Mathematics, no. 1004, Springer-Verlag, 1983, pp. 1–9.Google Scholar
[5] Bergman, C., Amalgamation classes of some distributive varieties, Algebra Universalis, vol. 20 (1985), pp. 143–166.Google Scholar
[6] Bruyns, P., Naturman, C., and Rose, H., Amalgamation in the pentagon variety, Algebra Universalis, vol. 29 (1992), pp. 303–322.Google Scholar
[7] Burris, S., Boolean powers, Algebra Universalis, vol. 5 (1975), pp. 341–360.CrossRefGoogle Scholar
[8] Burris, S., Boolean constructions, Universal algebra and lattice theory, proceedings, puebla 1982, Lecture Notes in Mathematics, no. 1004, Springer-Verlag, 1983, pp. 67–90.Google Scholar
[9] Chang, C. C. and Keisler, H. J., Model theory, Studies in Logic and the Foundations of Mathematics, no. 73, North-Holland, Amsterdam-London, 1978.Google Scholar
[10] Hodges, W., Model theory, Encyclopedia of Mathematics and its Applications, no. 42, Cambridge University Press, 1993.CrossRefGoogle Scholar
[11] Jipsen, P. and Rose, H., Absolute retracts and amalgamation in certain congruence distributive varieties, Canadian Mathematics Bulletin, vol. 32 (1989), pp. 309–313.CrossRefGoogle Scholar
[12] Mansfield, R., The theory of Boolean ultrapowers, Annals of Mathematical Logic, vol. 2 (1971), pp. 297–325.Google Scholar
[13] Monk, J. D. and Bonnet, R. (editors), Handbook of Boolean algebras, vol. 1–3, North-Holland, Amsterdam-New York-Oxford-Tokyo, 1989.Google Scholar
[14] Taylor, W., Residually small varieties, Algebra Universalis, vol. 2 (1972), pp. 33–53.CrossRefGoogle Scholar
[15] Yasuhara, M., The amalgamation property, the universal-homogeneous models and generic models, Mathematica Scandinavica, vol. 34 (1973), pp. 5–36.Google Scholar