[FOM] geometry and non-well-founded sets
Robert Lubarsky
robert.lubarsky at comcast.net
Fri Sep 14 06:47:11 EDT 2007
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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