Abstract
The so-called singular cardinal problem consists of the description of the possible size of the cardinal, \(X_\eta ^{cf\left( {{N_\eta }} \right)}\), that is ℶ(ℵ η ), the value of the gimel function at the argument ℵ η , for singular cardinals ℵ η . An estimate for this cardinal power is given by the Galvin-Hajnal theorem if ℵ η is an ℵ0-strong singular cardinal with uncountable cofinality. The centre of our investigations will be the Galvin-Hajnal formula, from which all other results on cardinals in this chapter will follow. For the first time it turns out that a profound cardinal property is a source of cardinal arithmetic.
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© 1999 Springer Basel AG
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Holz, M., Steffens, K., Weitz, E. (1999). The Galvin-Hajnal Theorem. In: Introduction to Cardinal Arithmetic. Modern Birkhäuser Classics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0346-0330-0_3
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DOI: https://doi.org/10.1007/978-3-0346-0330-0_3
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0346-0327-0
Online ISBN: 978-3-0346-0330-0
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