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Aleph–zero categorical Stone algebras

Published online by Cambridge University Press:  09 April 2009

Philip Olin
Philip Olin
Affiliation:
Department of Mathematics York University Downsview, Ontario Canada
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Abstract

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This paper is a contribution to the problem of characterizing the ℵ0-categorical Stone algebras. If the dense set is either finite or a chain, the problem is solved by reducing it to the ℵ0-categoricity of the skeleton and the dense set, solutions for these being known. If the dense set is a Boolean algebra, we show that this type of reduction works for certain subclasses but not for all such algebras. For generalized Post algebras the characterization problem is solved completely.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 26 , Issue 3 , November 1978 , pp. 337 - 347
Copyright
Copyright © Australian Mathematical Society 1978

References

Balbes, R. and Dwinger, P. (1974), Distributive Lattices (University of Missouri Press, Columbia, Missouri).Google Scholar
Baur, W., Cherlin, G. and Macintyre, A. (1977), “On totally categorical groups and rings” (preprint).Google Scholar
Burris, S. (1975), ‘Boolean powers”, Algebra Univ. 5, 341–360.Google Scholar
Chang, C. C. and Keisler, H. J. (1973), Model Theory (North-Holland Publishing Co., Amsterdam).Google Scholar
Chen, C. C. and Grätzer, G. (1969), “Stone lattices I: Construction theorems”, Canad. J. Math. 21, 884–894.CrossRefGoogle Scholar
Grätzer, G. (1971), Lattice Theory: First Concepts and Distributive Lattices (W. H. Freeman Co., San Francisco).Google Scholar
Quackenbush, R. W. (1972), “Free products of bounded distributive lattices”, Algebra Univ. 2, 393–394.CrossRefGoogle Scholar
Rosenstein, J. (1969), “ℵ0-categoricity of linear orderings”, Fund. Math. 64, 1–5.CrossRefGoogle Scholar
Rosenstein, J. (1973), “ℵ0-categoricity of groups”, J. of Algebra 25, 435–467.Google Scholar
Ryll-Nardzewski, C. (1959), “On the categoricity in power ≤ ℵ0”, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astro. Phys. 7, 545–548.Google Scholar
Sikorski, R. (1964), Boolean Algebras, 2nd ed. (Springer, Berlin).Google Scholar