[FOM] Reference request for category-theoretic presentation of forcing

[John Baldwin]

Neil,

I have no real idea about this but in looking around I stumbled over this
article

http://www.math.lsa.umich.edu/~ablass/interact.pdf

and it is hard for me think there is anyone who really understands both set
theory and category theory better than Andreas. so while this may not
address the forcing it may still be helpful. And of course you likely
already saw it.

Andreas and Colin McLarty would be two people to ask directly about this.

John

John T. Baldwin
Professor Emeritus
Department of Mathematics, Statistics,
and Computer Science M/C 249
jbaldwin at uic.edu
851 S. Morgan
Chicago IL
60607

On Mon, Jul 3, 2017 at 6:44 AM, Neil Barton <bartonna at gmail.com> wrote:

> Dear All,
>
> A short reference request: I'm interested in the category-theoretic
> presentations of set-theoretic forcing (e.g. showing that ~CH is consistent
> with ZFC).
>
> As someone with a reasonable knowledge of set theory (inner models and the
> forcing construction are certainly fine) and a basic knowledge of topos
> theory (subobject classifiers, algebras of subobjects, sheaves etc.) what's
> the best reference here? Would that be the Appendix to Bell's *Boolean-Valued
> Models and Independence Proofs*, or are there other references? I would
> like a little more detail on the wider implications of this way of cashing
> out the results, in particular how they relate to category theory/set
> theory more generally.
>
> Best Wishes,
>
> Neil
>
> --
> Dr. Neil Barton
> Postdoctoral Research Fellow
> Kurt Gödel Research Center for Mathematical Logic
> University of Vienna
>
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