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Topic: How much set theory is needed for geometry?
Replies: 5   Last Post: Feb 29, 2008 11:10 AM

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Frederick Williams

Posts: 239
Registered: 5/31/07
How much set theory is needed for geometry?
Posted: Feb 15, 2008 10:42 AM
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I make reference to Coxeter, _Introduction to Geometry_, Wiley, Second
edition.

In section 12.2 _Intermediacy_ , Coxeter discusses the relation
[ABC]--informally "point B is between points A and C"--and then he
defines segment, interval, ray and line as sets using that relation.

Not much set theory seems to be needed, but how much? If one were to
formalize this set theory should it be a theory with points as
Urelemente?

Would one do better to formalize it using many-sorted first order logic
with points, segments, intervals, rays and lines as sorts?

In either case, what then about triangles and other plane figures?

--
Going forward at this moment in time a raft of measures
have been put in place on the ground to target and
claw back the growth of cliche usage 24/7.
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