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Ternary Operations as Primitive Notions for Constructive Plane Geometry VI

✍ Scribed by Victor Pambuccian

Book ID
102941924
Publisher
John Wiley and Sons
Year
1995
Tongue
English
Weight
630 KB
Volume
41
Category
Article
ISSN
0044-3050

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✦ Synopsis

Abstract

In this paper we provide quantifier‐free, constructive axiomatizations for several fragments of plane Euclidean geometry over Euclidean fields, such that each axiom contains at most 4 variables. The languages in which they are expressed contain only at most ternary operations. In some precisely defined sense these axiomatizations are the simplest possible.

📜 SIMILAR VOLUMES

Ternary operations as primitive notions
Ternary operations as primitive notions for constructive plane geometry III
✍ Victor Pambuccian 📂 Article 📅 1993 🏛 John Wiley and Sons 🌐 English ⚖ 499 KB

## Abstract This paper continues the investigations begun in [6] and continued in [7] about quantifier‐free axiomatizations of plane Euclidean geometry using ternary operations. We show that plane Euclidean geometry over Archimedean ordered Euclidean fields can be axiomatized using only two ternary

Ternary Operations as Primitive Notions
Ternary Operations as Primitive Notions for Constructive Plane Geometry IV
✍ Victor Pambuccian 📂 Article 📅 1994 🏛 John Wiley and Sons 🌐 English ⚖ 490 KB

## 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’

TERNARY OPERATIONS AS PRIMITIVE NOTIONS
TERNARY OPERATIONS AS PRIMITIVE NOTIONS FOR PLANE GEOMETRY II
✍ Victor Pambuccian 📂 Article 📅 1992 🏛 John Wiley and Sons 🌐 English ⚖ 197 KB

## Abstract We proved in the first part [1] that plane geometry over Pythagorean fields is axiomatizable by quantifier‐free axioms in a language with three individual constants, one binary and three ternary operation symbols. In this paper we prove that two of these operation symbols are superfluou