Some arguments in Favor of the Continuum Hypothesis

[Noah Schweber]

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 aol.com> wrote:

> FOM:
>
> I have just uploaded a manuscript
>  Some arguments in Favor of the Continuum Hypothesis
>  https://www.researchgate.net/publication/363885503
>
> 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
>
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