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Chains and antichains in interval algebras

Published online by Cambridge University Press:  12 March 2014

M. Bekkali
M. Bekkali*
Affiliation:
P. O. Box 3454, Boulder, Colorado 80307
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Abstract

Let κ be a regular cardinal, and let B be a subalgebra of an interval algebra of size κ. The existence of a chain or an antichain of size κ in ℬ is due to M. Rubin (see [7]). We show that if the density of B is countable, then the same conclusion holds without this assumption on κ. Next we also show that this is the best possible result by showing that it is consistent with 2ℵ0 = ℵω1 that there is a boolean algebra B of size ℵω1 such that length(B) = ℵω1 is not attained and the incomparability of B is less than ℵω1. Notice that B is a subalgebra of an interval algebra. For more on chains and antichains in boolean algebras see. e.g., [1] and [2].

Keywords

Tree algebrainterval algebraorder set
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 59 , Issue 3 , September 1994 , pp. 860 - 867
Copyright
Copyright © Association for Symbolic Logic 1994

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References

REFERENCES

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