[FOM] geometry and non-well-founded sets

Thomas Forster T.Forster at dpmms.cam.ac.uk
Thu Sep 13 17:39:21 EDT 2007


I don't know a reference, but this sounds like a simple application of 
known results.  Try Barwise & E, Vicious Circle: you need what they call 
the *Solution Lemma*.  Rather a cute application come to think of it - and
one i hadn't thought of.   

 If you get more precise details do tell me


> Someone once said to me (and it sounds true) that using a 
> non-well-founded set theory you could so axiomatize projective 
> geometry that *both* a line is identified with the set of points 
> lying on it *and* a point is identified with the pencil of lines 
> passing through it. Can anyone give me a reference for somewhere this 
> is actually done?
> Robert
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