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Joel David Hamkins
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In ZFCA, every set is equinumerous with a pure set, since every well ordering of a set makes it bijective with an ordinal, which is pure. Therefore the cardinal structure of any model of ZFCA is reflected in its pure sets, and in particular, CH and the GCH will hold, respectively, if and only if it holdsthey hold in the underlying ZFC model of pure sets.

In ZFCA, every set is equinumerous with a pure set, since every well ordering of a set makes it bijective with an ordinal, which is pure. Therefore the cardinal structure of any model of ZFCA is reflected in its pure sets, and in particular, CH and the GCH will hold if and only if it holds in the underlying ZFC model of pure sets.

In ZFCA, every set is equinumerous with a pure set, since every well ordering of a set makes it bijective with an ordinal, which is pure. Therefore the cardinal structure of any model of ZFCA is reflected in its pure sets, and in particular, CH and the GCH will hold, respectively, if and only if they hold in the underlying ZFC model of pure sets.

Source Link
Joel David Hamkins
  • 236.3k
  • 44
  • 777
  • 1.4k

In ZFCA, every set is equinumerous with a pure set, since every well ordering of a set makes it bijective with an ordinal, which is pure. Therefore the cardinal structure of any model of ZFCA is reflected in its pure sets, and in particular, CH and the GCH will hold if and only if it holds in the underlying ZFC model of pure sets.