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DECISION PROBLEMS IN EUCLIDEAN GEOMETRY

By Harvey M. Friedman

Abstract

Abstract. We show the algorithmic unsolvability of a number of decision procedures in ordinary two dimensional Euclidean geometry, involving lines and integer points. We also consider formulations involving integral domains of characteristic 0, and ordered rings. The main tool is the solution to Hilbert's Tenth Problem. The limited number of facts used from recursion theory are isolated at the beginning

Year: 2010
OAI identifier: oai:CiteSeerX.psu:10.1.1.353.2712
Provided by: CiteSeerX
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