Infinite antichains in semilattices
Document Type
Article
Publication Date
9-1-1985
Abstract
In this paper we consider infinite antichains and the semilattices that they generate, mainly in the context of continuous semilattices. Conditions are first considered that lead to the antichain generating a copy of a countable product of the two-element semilattice. Then a special semilattice, called Δ, is defined, its basic properties developed, and it is shown in our main result that a continuous semilattice with an infinite antichain converging to a larger element contains a semilattice copy of Δ. The paper closes with a consideration of countable antichains that converge to a lower element or a parallel element and the kinds of semilattices generated in this context. © 1985 D. Reidel Publishing Company.
Publication Source (Journal or Book title)
Order
First Page
275
Last Page
290
Recommended Citation
Lawson, J., Mislove, M., & Priestley, H. (1985). Infinite antichains in semilattices. Order, 2 (3), 275-290. https://doi.org/10.1007/BF00333134