Why are surjective lineations of the archimedean hyperbolic plane motions?

Victor Pambuccian

doi:10.1023/A:1024652016885

Why are surjective lineations of the archimedean hyperbolic plane motions?

Victor Pambuccian

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

4 Scopus citations

Abstract

Positive ℒ_ω1ω definitions of point-inequality and noncollinearity in terms of collinearity, which are valid in plane hyperbolic geometry over arbitrary Archimedean ordered Euclidean fields, provide a synthetic proof of the theorem stated in the title and first noticed to be a corollary of a result from by R. Höfer.

Original language	English (US)
Pages (from-to)	63-67
Number of pages	5
Journal	Acta Mathematica Hungarica
Volume	100
Issue number	1-2
DOIs	https://doi.org/10.1023/A:1024652016885
State	Published - Jul 2003

Keywords

Definability
Hyperbolic geometry
ℒ-logic

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1023/A:1024652016885

Cite this

@article{f8e69aa27ec84d47b1c50e7f9c12a014,

title = "Why are surjective lineations of the archimedean hyperbolic plane motions?",

abstract = "Positive ℒω1ω definitions of point-inequality and noncollinearity in terms of collinearity, which are valid in plane hyperbolic geometry over arbitrary Archimedean ordered Euclidean fields, provide a synthetic proof of the theorem stated in the title and first noticed to be a corollary of a result from by R. H{\"o}fer.",

keywords = "Definability, Hyperbolic geometry, ℒ-logic",

author = "Victor Pambuccian",

year = "2003",

month = jul,

doi = "10.1023/A:1024652016885",

language = "English (US)",

volume = "100",

pages = "63--67",

journal = "Acta Mathematica Hungarica",

issn = "0236-5294",