Re: Paper and slides on indefiniteness of CH

Dear Bob,

Here is a precise statement. Suppose every set X belongs to an inner model of a measurable Woodin (above X).

Suppose there is a club class C of cardinals such that for all \gamma \in C,

(V_{\gamma},C\cap \gamma) \not\vDash \textsf{ZFC}

Then there is an inner model N of V such that N \vDash \textsf{ZFC + GCH} and such that V is a class-generic extension of N.

(Nothing special about GCH here).  Though here one can require that N is a fine-structure model if one wants.

The class C can always be forced without adding sets.

If one has inner model theory for measurable Woodin cardinals then the class C is unnecessary.

Regards,
Hugh

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <strike> <strong>