Chain Conditions in the Distributive Free Product of Lattices
نویسنده
چکیده
1. Introduction. A typical result of this paper is the following. Let Lt, i e I be distributive lattices satisfying the countable chain condition. Then the free product L of these lattices also satisfies the countable chain condition. To be able to state the general result we need some notations. Let trt be an infinite cardinal. A poset (partially ordered set) P is said to satisfy the m-chain condition if every chain in P has cardinality < m. (Thus the countable chain condition is the Si-chain condition.) Given a category of lattices that admits free products, a cardinal n>l, and an infinite cardinal m we define condition
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