An ordinal a is equal to the set of its predecessors and is ordered by the membership relation. For any ordinal a, one writes a -~ (a, m) 2 if and only if for any set A order-isomorphic to a, and any function f from the pairs of elements of A into {0, 1}, either there is a subset X c\_ A order-isomo
A partition theorem for ordinals
β Scribed by Diana Schmidt
- Publisher
- Elsevier Science
- Year
- 1979
- Tongue
- English
- Weight
- 138 KB
- Volume
- 27
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
For ordinals :, ;, and #, the expression : Γ % ( ;, #) 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
B THEOREM ON DEFINITIONS O F THE ZERMELO-NEUMANN ORDINALS'l) by HAO WANG in Cambridge, Mass. (USA)
A key identity in three free parameters involving partitions into distinct parts is proved using Jackson's q-analog of Dougall's summation. This identity is shown to be combinatorially equivalent to a reformulation of a deep partition theorem of Go llnitz obtained by the use of a quartic transformat