Israel Journal of Mathematics

, Volume 35, Issue 1, pp 61-88

First online:

All uncountable cardinals can be singular

  • M. GitikAffiliated withInstitute of Mathematics, The Hebrew University of Jerusalem

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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.