Some arguments in Favor of the Continuum Hypothesis

Noah Schweber schweber at
Thu Sep 29 21:18:13 EDT 2022

Unless I'm missing something, the existence of a nontrivial elementary
embedding of L into L is upwards absolute since M computes L correctly.
(Another argument: 0# is a Pi^1_2 singleton, so M's 0# satisfies the
relevant Pi^1_2 formula in V as well due to Shoenfield absoluteness.)

On Thu, Sep 29, 2022 at 5:38 PM <martdowd at> wrote:

> FOM:
> I have just uploaded a manuscript
>  Some arguments in Favor of the Continuum Hypothesis
> This is in progress, but i have uploaded it as is, and will send another
> post to FOM when the completed version is uploaded.  Any comments would be
> appreciated, especially if I could incorporate them.
> Does anyone know of a proof that 0# follows from PFA (proper forcing
> axiom)?  From results I have seen quoted, there's an inner model M with a
> Woodin cardinal, hence a measurable cardinal, and hence 0# is true in M.
> This means that in M there is a non-trivial embedding of L in L, and I
> suspect this means there is such in V.
> Martin Dowd
-------------- next part --------------
An HTML attachment was scrubbed...
URL: </pipermail/fom/attachments/20220929/ccbab96f/attachment-0001.html>

More information about the FOM mailing list