K-theory and sets

martdowd at aol.com martdowd at aol.com
Sat Jun 4 23:05:16 EDT 2022

Monroe Eskew writes:

Could you elaborate on this claim? 
 Well, although it doesn't directly address the question, in general a main dichotomy in extensions of ZFC is whether V=L.  With the  great success of core model theory the case against it has been strengthened.  However a few die-hards still think that even this is inconclusive, and the question remains as mystifying as ever.  Indeed, if 0# exists then one can construct K^DJ.  But this isn't really evidence that it does.
Martin Dowd
-----Original Message-----
From: Monroe Eskew <monroe.eskew at univie.ac.at>
To: Foundations of Mathematics <fom at cs.nyu.edu>
Sent: Fri, Jun 3, 2022 9:55 pm
Subject: Re: K-theory and sets

> On 04.06.2022, at 06:15, Ignacio Añón <ianon at latahona.com.uy> wrote:
> The type of set theory that best formalizes these ideas, is of a particular vintage: it is best represented by set theorists like Cantor, Hausdorff, Godel, Takeuti, Todercevic, and ill represented by set theorists in the vein of Solovay, Woodin, Kunen, Dales...
> Putting forward the notion that set theory is a simple, unified foundational field vis a vis Category theory, falsifies the richness of traditions and ideas within set theory: Kanamori's bitingly lucid pieces show this with stark clarity...
> Foundationally, different traditions within set theory differ, in their outlook, much more so than set theory and category theory. 

Could you elaborate on this claim? In what way do Todorcevic and Woodin come from “different traditions” in set theory?  What writings of Kanamori support this claim, and how?
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