The non-planarity of K5 and K3,3 as axioms for plane ordered geometry

Victor Pambuccian

doi:10.1007/s00022-012-0129-z

The non-planarity of K₅ and K_3,3 as axioms for plane ordered geometry

Victor Pambuccian

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

1 Scopus citations

Abstract

The Pasch axiom is shown to be equivalent, given the linear order axioms, to the conjunction of its outer form with the statement that K₅ (or K_3,3) is not planar.

Original language	English (US)
Pages (from-to)	313-318
Number of pages	6
Journal	Journal of Geometry
Volume	103
Issue number	2
DOIs	https://doi.org/10.1007/s00022-012-0129-z
State	Published - Aug 2012

Keywords

The Pasch axiom
non-planarity
ordered planes
splitting an axiom
the outer form of the Pasch axiom

ASJC Scopus subject areas

Geometry and Topology

Access to Document

10.1007/s00022-012-0129-z

Cite this

@article{2dbdb756b3f343f68f9f1a14e6fb8651,

title = "The non-planarity of K5 and K3,3 as axioms for plane ordered geometry",

abstract = "The Pasch axiom is shown to be equivalent, given the linear order axioms, to the conjunction of its outer form with the statement that K5 (or K3,3) is not planar.",

keywords = "The Pasch axiom, non-planarity, ordered planes, splitting an axiom, the outer form of the Pasch axiom",

author = "Victor Pambuccian",

year = "2012",

month = aug,

doi = "10.1007/s00022-012-0129-z",

language = "English (US)",

volume = "103",

pages = "313--318",

journal = "Journal of Geometry",

issn = "0047-2468",

publisher = "Birkhauser Verlag Basel",

number = "2",

}

TY - JOUR

T1 - The non-planarity of K5 and K3,3 as axioms for plane ordered geometry

AU - Pambuccian, Victor

PY - 2012/8

Y1 - 2012/8

N2 - The Pasch axiom is shown to be equivalent, given the linear order axioms, to the conjunction of its outer form with the statement that K5 (or K3,3) is not planar.

AB - The Pasch axiom is shown to be equivalent, given the linear order axioms, to the conjunction of its outer form with the statement that K5 (or K3,3) is not planar.

KW - The Pasch axiom

KW - non-planarity

KW - ordered planes

KW - splitting an axiom

KW - the outer form of the Pasch axiom

UR - http://www.scopus.com/inward/record.url?scp=84869199084&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84869199084&partnerID=8YFLogxK

U2 - 10.1007/s00022-012-0129-z

DO - 10.1007/s00022-012-0129-z

M3 - Article

AN - SCOPUS:84869199084

SN - 0047-2468

VL - 103

SP - 313

EP - 318

JO - Journal of Geometry

JF - Journal of Geometry

IS - 2

ER -