[FOM] concerning surjection from S^2 onto Pow(S)

Harvey Friedman hmflogic at gmail.com
Fri Oct 19 00:36:57 EDT 2012

Concerning that equivalence in


When I posted that message on the FOM, I had assumed that the status
of the equivalence in ZF was known, and was expecting someone to give
me a reference.

So let me now state explicitly that although the equivalence is
obviously provable in ZFC (Replacement not needed), I do not know if
it is provable in ZF.

I expect that it is not provable in ZF.

To summarize, I expect that ZF does not prove that the following are equivalent:

1. there is a surjective map from S x S onto Pow(S).
2. S has exactly two, three, or four elements.

Harvey Friedman

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