Series: Penn State Logic Seminar
Date: Tuesday, September 19, 2000
Time: 2:30 - 3:20 PM
Place: 307 Boucke Building
Speaker: Stephen G. Simpson, Department of Mathematics, Penn State
Title: Axiomatic Geometry
Abstract:
Tarski has given an explicit axiomatization of the complete,
first-order theory RCOF of the ordered field of real numbers.
Consequently, RCOF is decidable. I note that first-order Euclidean
plane geometry is interpretable in RCOF, and is therefore decidable.
Thus Euclidean plane geometry is in a sense reducible to real
arithmetic. In addition, I present Tarski's explicit, complete
axiomatization of Euclidean plane geometry. I indicate the
modifications needed for hyperbolic (Lobachevskian) plane geometry,
and for the Euclidean and hyperbolic geometries of dimension n, where
n is a positive integer.