Israel Journal of Mathematics

, Volume 35, Issue 1, pp 61–88

All uncountable cardinals can be singular


  • M. Gitik
    • Institute of MathematicsThe Hebrew University of Jerusalem

DOI: 10.1007/BF02760939

Cite this article as:
Gitik, M. Israel J. Math. (1980) 35: 61. doi:10.1007/BF02760939


Assuming the consistency of the existence of arbitrarily large strongly compact cardinals, we prove the consistency with ZF of the statement that every infinite set is a countable union of sets of smaller cardinality. Some other statements related to this one are investigated too.

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© The Weizmann Science Press of Israel 1980