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Products of chains with monochromatic maximal chains and antichains

✍ Scribed by D. Duffus; T. Goddard

Publisher
Springer Netherlands
Year
1996
Tongue
English
Weight
996 KB
Volume
13
Category
Article
ISSN
0167-8094

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✦ Synopsis

There is a product of two linear orders of size 2nn with the property that every subset or complement thereof contains a maximal chain. Furthermore, for regular l&, there is a product of two linear orders of size t&+2 that when colored with fewer than & colors always has a monochromatic maximal chain. As a corollary, for every uncountable strong limit cardinal K,, there is an ordered set of cardinality K that must be colored with at least K colors before no monochromatic maximal chains are present. Duals of these results show that at least as much is true for maximal antichains.

Mathematics

Subject Classification (1991). 06AlO.

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