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Negative Partition Relations for Ordinals ωωα

✍ Scribed by Carl Darby

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
177 KB
Volume
76
Category
Article
ISSN
0095-8956

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✦ Synopsis

For ordinals :, ;, and #, the expression : Ä % ( ;, #) 2 means there is a partition of the pairs from :, [:] 2 =2 0 _ 2 1 such that for any X :, if the order type of X is ; then [X] 2 3 2 0 and if the order type of X is # then [X] 2 3 2 1 . It is shown that if :<| 1 is multiplicatively decomposable, then | : Ä % (| : , n) 2 for n=4 or n=6, depending on the degree of decomposability of :.

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