𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Ternary operations as primitive notions for constructive plane geometry III

✍ Scribed by Victor Pambuccian

Publisher
John Wiley and Sons
Year
1993
Tongue
English
Weight
499 KB
Volume
39
Category
Article
ISSN
0044-3050

No coin nor oath required. For personal study only.

✦ Synopsis

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 operations if one allows axioms that are not first‐order but universal L~w1,w~ sentences. The operations are: the transport of a segment on a halfline that starts at one of the endpoints of the given segment, and the operation which produces one of the intersection points of a perpendicular on a diameter of a circle (which intersects that diameter at a point inside the circle) with that circle. MSC: 03F65, 51M05, 51M15.

📜 SIMILAR VOLUMES

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