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Erdős-Rado without choice

Published online by Cambridge University Press:  12 March 2014

Thomas Forster
Thomas Forster*
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 OWB., UK. E-mail: T.Forster@dpmms.cam.ac.uk
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Abstract

A version of the Erdős-Rado theorem on partitions of the unordered n-tuples from uncountable sets is proved, without using the axiom of choice. The case with exponent 1 is just the Sierpinski-Hartogs' result that .

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 72 , Issue 3 , September 2007 , pp. 897 - 900
Copyright
Copyright © Association for Symbolic Logic 2007

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References

[1] Erdős, P., Some set-theoretical properties of graphs. Revista Universidad Nacional de Tucuman, Serie A, vol. 3 (1942), pp. 363–367.Google Scholar
[2] Erdős, P. and Rado, R., A partition calculus in set theory, The Bulletin of the American Mathematical Society, (1956), pp. 427–498.Google Scholar