[FOM] Undecidability in geometry

richman@fau.edu richman at fau.edu
Fri Nov 1 13:34:39 EST 2002

Matthew Frank pointed out to me that Euclid's axioms have a
model consisting only of the constructible points.

Of course Hilbert's "Axiom of line completeness" does not
hold in this model, but then neither God nor Euclid
introduced that axiom into geometry.

On balance, I think it fair to say that the proposition that
there exists a 20 degree angle is undecidable in Euclidean


More information about the FOM mailing list