Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-30T23:08:28.394Z Has data issue: false hasContentIssue false
  • English
  • Français

Weak cylindric set algebras and weak subdirect indecomposability

Published online by Cambridge University Press:  12 March 2014

H. Andréka ,
I. Németi  and
R. J. Thompson
H. Andréka
Affiliation:
Mathematical Institute, Hungarian Academy of Sciences, 1364 Budapest, Hungary
I. Németi
Affiliation:
Mathematical Institute, Hungarian Academy of Sciences, 1364 Budapest, Hungary
R. J. Thompson
Affiliation:
Mathematical Institute, Hungarian Academy of Sciences, 1364 Budapest, Hungary
Get access Rights & Permissions [Opens in a new window]

Abstract

In this note we prove that the abstract property “weakly subdirectly indecomposable” does not characterize the class IWsα of weak cylindric set algebras. However, we give another (similar) abstract property characterizing IWsα. The original property does characterize the directed unions of members of IWsα iff α is countable. Free algebras will be shown to satisfy the original property.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 55 , Issue 2 , June 1990 , pp. 577 - 588
Copyright
Copyright © Association for Symbolic Logic 1990

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[AN83]Andréka, H. and Németi, I., IWsα is not characterized by weak subdirect indecomposability and is not closed under directed unions either, preprint, 1983.Google Scholar
[G88]Goldblatt, R., On closure under canonical embedding algebras, Algebraic logic (proceedings, Budapest, 1988), Colloquia Mathematica Societatis János Bolyai, North-Holland, Amsterdam (to appear).Google Scholar
[HMTAN]Henkin, L., Monk, J. D., Tarski, A., Andréka, H. and Németi, I., Cylindric set algebras, Lecture Notes in Mathematics, vol. 883, Springer-Verlag, Berlin, 1981.CrossRefGoogle Scholar
[HMTI]Henkin, L., Monk, J. D. and Tarski, A., Cylindric algebras, Part I, North-Holland, Amsterdam, 1971.Google Scholar
[HMTII]Henkin, L., Monk, J. D. and Tarski, A., Cylindric algebras, Part II, North-Holland, Amsterdam, 1985.Google Scholar
[HMT81]Henkin, L., Monk, J. D. and Tarski, A., Cylindric set algebras and related structures, in [HMTAN], pp. 1–129.CrossRefGoogle Scholar