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

Noah Schweber schweber at berkeley.edu
Mon Jul 3 18:06:32 EDT 2017

I believe the standard source here is "Sheaves in geometry and logic" by
Maclane and Moerdijk - specifically, chapter VI.

On Mon, Jul 3, 2017 at 4:44 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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