K-theory and sets

[Monroe Eskew]

> 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?