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- W2183065700 abstract "Let I and μ be an infinite index set and a cardinal, respectively, such that |I| ≤ μ and, starting from ℵ0, μ can be constructed in countably many steps by passing from a cardinal λ to 2λ at successor ordinals and forming suprema at limit ordinals. We prove that there exists a system X = {Li: i ∈ I} of complemented lattices of cardinalities less than |I| such that if i, j ∈ I and φ: Li → Lj is an order embedding, then i = j and φ is the identity map of Li. If |I| is countable, then, in addition, X consists of finite lattices of length 10. Stating the main result in other words, we prove that the category of (complemented) lattices with order embeddings has a discrete full subcategory with |I| many objects. Still in other words, the class of these lattices has large antichains (that is, antichains of size |I|) with respect to the quasiorder “embeddability.” As corollaries, we trivially obtain analogous statements for partially ordered sets and semilattices." @default.
- W2183065700 created "2016-06-24" @default.
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- W2183065700 date "2015-11-30" @default.
- W2183065700 modified "2023-09-27" @default.
- W2183065700 title "Large Sets of Lattices without Order Embeddings" @default.
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- W2183065700 doi "https://doi.org/10.1080/00927872.2014.967352" @default.
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