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On the cardinality of ultraproduct of finite sets

Published online by Cambridge University Press:  12 March 2014

Saharon Shelah*
Hebrew University of Jerusalem


We shall prove that if is an ultrafilter and λ ℵ0 = λ. This affirms a conjecture of Keisler.

Research Article
Copyright © Association for Symbolic Logic 1970

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[1] Frayne, T., Morel, A. and Scott, D., Reduced direct products, Fundamenta mathematicae, vol. 51 (1962), pp. 195248.CrossRefGoogle Scholar
[2] Keisler, H. J., Ultraproducts of finite sets, this Journal, vol. 32 (1967), pp. 4757.Google Scholar