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Strong partition properties for infinite cardinals

Published online by Cambridge University Press:  12 March 2014

E. M. Kleinberg
E. M. Kleinberg*
Affiliation:
The Rockefeller University Massachusetts Institute of Technology
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Extract

The notion of a “partition relation”, as it has been studied in the context of set theory for the past several years, was inspired by the following theorem of F. P. Ramsey [14]:

Theorem 0.1. Let n be a positive integer and let {A, B} be a partition of those subsets of the nonnegative integers containing exactly n elements. Then there exists an infinite subset x of the nonnegative integers all of whose n-element subsets are contained in only one of A or B. (Any such set x is said to be “homogeneous” for the partition.)

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 35 , Issue 3 , September 1970 , pp. 410 - 428
Copyright
Copyright © Association for Symbolic Logic 1971

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