Violating the singular cardinals hypothesis without large cardinals

Moti Gitik, Peter Koepke

Research output: Contribution to journalArticlepeer-review


We extend a transitive model V of ZFC+GCH cardinal preservingly to a model N of ZF + "GCH holds below אω" + "there is a surjection from the power set of אω onto λ", where λ is an arbitrarily high fixed cardinal in V. The construction can be described as follows: add אn+1 many Cohen subsets of אn+1 for every n < ω, and adjoin λ many subsets of אω which are unions of ω-sequences of those Cohen subsets; then let N be a choiceless submodel generated by equivalence classes of the λ subsets of אω modulo an appropriate equivalence relation.

Original languageEnglish
Pages (from-to)901-922
Number of pages22
JournalIsrael Journal of Mathematics
Issue number2
StatePublished - Sep 2012


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