Mathematical Logic Quarterly

Ternary Operations as Primitive Notions for Constructive Plane Geometry IV

Journal Article

Abstract

In this paper we provide a quantifier‐free constructive axiomatization for Euclidean planes in a first‐order language with only ternary operation symbols and three constant symbols (to be interpreted as ‘points’). We also determine the algorithmic theories of some ‘naturally occurring’ plane geometries.

Mathematics Subject Classification: 03F65, 51M05, 51M15, 03B30.

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