Hostname: page-component-84b7d79bbc-g7rbq Total loading time: 0 Render date: 2024-07-27T14:03:18.217Z Has data issue: false hasContentIssue false
  • English
  • Français

Boolean-valued equivalence relations and complete extensions of complete boolean algebras

Published online by Cambridge University Press:  17 April 2009

Denis Higgs
Denis Higgs
Affiliation:
University of Waterloo, Waterloo, Ontario, Canada.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is remarked that, if A is a complete boolean algebra and δ is an A-valued equivalence relation on a non-empty set I, then the set of δ-extensional functions from I to A can be regarded as a complete boolean algebra extension of A and a characterization is given of the complete extensions which arise in this way.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 3 , Issue 1 , August 1970 , pp. 65 - 72
Copyright
Copyright © Australian Mathematical Society 1970

References

[1] Ellis, David and Sprinkle, H.D., “Topology of B-metric spaces”, Compositio Math. 12 (1954/1956), 250–262.Google Scholar
[2] Grätzer, George, Universal algebra (Van Hostrand, Princeton, New Jersey, Toronto, London, Melbourne, 1968).Google Scholar
[3] Halmos, Paul R., “Algebraic logic, I. Monadic boolean algebras”, Campositio Math. 12 (1954/1956), 217–249.Google Scholar
[4] Higgs, D.A., “Matroids and duality”, Colloq. Math. 20 (1969), 215–220.CrossRefGoogle Scholar
[5] Łoś, Jerzy, “Quelques remarques, théorèmes et problèmes sur les classes définissables d'algèbres”. Mathematical interpretation of formal systems, 98–113. (North-Holland, Amsterdam, 1955).CrossRefGoogle Scholar
[6] Rubin, Jean E., “Remarks about a closure algebra in which closed elements are open”, Proc. Amer. Math. Soc. 7 (1956), 30–34.CrossRefGoogle Scholar