A cofinal coloring theorem for partially ordered algebras
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If P is a directed partially ordered algebra of an appropriate sort-e.g. an upper semilattice-and has no maximal element, then P has two disjoint subalgebras each cofinal in P. In fact, if P has cofinality α then there exists a family of α such disjoint subalgebras. A version of this result is also proved without the directedness assumption, in which the cofinality of P is replaced by an invariant which we call its global cofinality.
AMS (MOS) subject classifications (1980)Primary: 06A10, 06A12, 06F99 secondary: 04A10, 04A20, 06B05, 06F05
Key wordsPartially ordered algebra disjoint cofinal subalgebras lattice semilattice cofinality (resp. global cofinality) of a partially ordered set
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