[FOM] geometry and non-well-founded sets

[Robert Lubarsky]

A different way of modeling this is with modal set theory. You could be in a
state where, say, a line is a set of points, and necessarily (i.e. at all
accessible states) a point is a set of line; and vice versa. Viewed
model-theoretically, the interpretation of a point keeps flip-flopping
between these two possibilities.

Bob Lubarsky


-----Original Message-----
From: fom-bounces at cs.nyu.edu [mailto:fom-bounces at cs.nyu.edu] On Behalf Of
Robert Black
Sent: Thursday, September 13, 2007 3:36 AM
To: fom at cs.nyu.edu
Subject: [FOM] geometry and non-well-founded sets

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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