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Powers of singular cardinals. (Spanish) Zbl 1116.03331
Contreras, G. (ed.) et al., 34th national congress of the Mexican Mathematical Society, Toluca, Mexico, October 7–12, 2001. Proceedings. México: Sociedad Matemática Mexicana (ISBN 970-32-0225-X/pbk). Aportaciones Mat., Comun. 30, 215-231 (2002).
This expository article, written in Spanish, contains results of F. Galvin and A. Hajnal on bounds for the cardinality of certain products of cardinals [Ann. Math. (2) 101, 491–498 (1975; Zbl 0327.02055)]. The presentation follows the book by P. Erdős, A. Hajnal, A. Máté and R. Rado [Combinatorial set theory: partition relations for cardinals. North-Holland, Amsterdam (1984; Zbl 0573.03019)]; the author views her article as an invitation to read this book. Special care is taken in presenting the combinatorial concepts used in the proofs. Generalizations of Silver’s result on powers of singular cardinals of uncountable cofinality are obtained as corollaries, but, instead of giving the results in their full generality, as they appear in the book just mentioned, the author presents them for the particular case of \(\aleph_{\omega_1}\) to reduce notational complications.
For the entire collection see [Zbl 1003.00012].
MSC:
03E10 Ordinal and cardinal numbers
03E05 Other combinatorial set theory
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