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

Neil Barton bartonna at gmail.com
Mon Jul 3 07:44:14 EDT 2017

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,


Dr. Neil Barton
Postdoctoral Research Fellow
Kurt Gödel Research Center for Mathematical Logic
University of Vienna
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