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

Robert Lubarsky lubarsky.robert at comcast.net
Mon Jul 3 21:47:14 EDT 2017

The one back in my day was Blass-Scedrov, Freyd’s Models for  the Independence of  AC, AMS memoir, http://bookstore.ams.org/memo-79-404/.


A much more modern presentation, less tied to any considerations of set theory, and inclusive of constructive (i.e. intuitionistic) forcing, is Mac-Lane-Moerdijk, Sheaves in Geometry and Logic (Springer). 


Given the example you cite (about CH), I’d think the former book is more what you’re looking for. 


Bob Lubarsky


From: fom-bounces at cs.nyu.edu [mailto:fom-bounces at cs.nyu.edu] On Behalf Of Neil Barton
Sent: Monday, July 3, 2017 7:44 AM
To: Foundations of Mathematics <fom at cs.nyu.edu>
Subject: [FOM] Reference request for category-theoretic presentation of forcing


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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