Ternary Operations as Primitive Notions for Constructive Plane Geometry VI

Victor Pambuccian

doi:10.1002/malq.19950410310

Ternary Operations as Primitive Notions for Constructive Plane Geometry VI

Victor Pambuccian

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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.

Original language	English (US)
Pages (from-to)	384-394
Number of pages	11
Journal	Mathematical Logic Quarterly
Volume	41
Issue number	3
DOIs	https://doi.org/10.1002/malq.19950410310
State	Published - 1995

Keywords

Cartesian Plane
Constructive axiomatization
Euclidean Plane
Ordered Euclidean Plane
Plane Euclidean geometry

ASJC Scopus subject areas

Logic

Access to Document

10.1002/malq.19950410310

Cite this

@article{136d9fe35e81492a80e9dfd7084ba1c7,

title = "Ternary Operations as Primitive Notions for Constructive Plane Geometry VI",

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.",

keywords = "Cartesian Plane, Constructive axiomatization, Euclidean Plane, Ordered Euclidean Plane, Plane Euclidean geometry",

author = "Victor Pambuccian",

year = "1995",

doi = "10.1002/malq.19950410310",

language = "English (US)",

volume = "41",

pages = "384--394",

journal = "Mathematical Logic Quarterly",

issn = "0942-5616",

publisher = "Wiley-VCH Verlag",

number = "3",

}

TY - JOUR

T1 - Ternary Operations as Primitive Notions for Constructive Plane Geometry VI

AU - Pambuccian, Victor

PY - 1995

Y1 - 1995

N2 - 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.

AB - 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.

KW - Cartesian Plane

KW - Constructive axiomatization

KW - Euclidean Plane

KW - Ordered Euclidean Plane

KW - Plane Euclidean geometry

UR - http://www.scopus.com/inward/record.url?scp=84981440865&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84981440865&partnerID=8YFLogxK

U2 - 10.1002/malq.19950410310

DO - 10.1002/malq.19950410310

M3 - Article

AN - SCOPUS:84981440865

VL - 41

SP - 384

EP - 394

JO - Mathematical Logic Quarterly

JF - Mathematical Logic Quarterly

SN - 0942-5616

IS - 3

ER -

Ternary Operations as Primitive Notions for Constructive Plane Geometry VI

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this