K-theory and sets

Monroe Eskew monroe.eskew at univie.ac.at
Mon Jun 6 00:55:27 EDT 2022

> On 06.06.2022, at 01:30, Ignacio Añón <ianon at latahona.com.uy> wrote:
> With regard to your concrete point about Woodin and Todorcevic: it is clear that Woodin, like Kunen and Solovay, takes for granted the results in(***), and works with inner models as if there are arbitrary large, consistent, values for 2^Aleph_alpha. Todorcevic, on the other hand, has investigated with care Gödel's axioms in search for a concrete, quasi topological, limit for the continuum(****). His work is quite relevant in complex analytic number theory, not just in fom.
The consistency of an arbitrarily large value of the continuum was established definitively by Cohen. I guarantee you that Todorcevic fully accepts this result. He is a master of forcing. He might see forcing axioms like PFA that imply the value of the continuum to be aleph2 as Platonically true, while acknowledging that different scenarios are consistent. 
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