Israel Journal of Mathematics

, Volume 35, Issue 1–2, pp 61–88 | Cite as

All uncountable cardinals can be singular

  • M. Gitik
Article

Abstract

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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Copyright information

© The Weizmann Science Press of Israel 1980

Authors and Affiliations

  • M. Gitik
    • 1
  1. 1.Institute of MathematicsThe Hebrew University of JerusalemJerusalemIsrael

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