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The independence of Ramsey's theorem

Published online by Cambridge University Press:  12 March 2014

E. M. Kleinberg
E. M. Kleinberg*
Affiliation:
The Rockefeller University
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Extract

In [3] F. P. Ramsey proved as a theorem of Zermelo-Fraenkel set theory (ZF) with the Axiom of Choice (AC) the following result:

(1) Theorem. Let A be an infinite class. For each integer n and partition {X, Y} of the size n subsets of A, there exists an infinite subclass of A all of whose size n subsets are contained in only one of X or Y.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 34 , Issue 2 , 25 July 1969 , pp. 205 - 206
Copyright
Copyright © Association for Symbolic Logic 1969

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References

[1] Cohen, P. J., Set theory and the continuum hypothesis, Benjamin, New York, 1966.Google Scholar
[2] Gödel, K., Consistency-proof for the generalized continuum hypothesis, Proceedings of the National Academy of Sciences of the U.S.A., vol. 25 (1939), pp. 220–224.Google Scholar
[3] Ramsey, F. P., On a problem of formal logic, Proceedings of the London Mathematical Society, vol. 30 (1929), Ser. 2, pp. 264–286.Google Scholar
[4] Shoenfield, J. R., The problem of predicatvity, Essays on the foundations of mathematics, pp. 132–139, Jerusalem, 1961.Google Scholar