7 Citations (Scopus)

Abstract

We show that the first-order theory of a large class of plane geometries and the first-order theory of their groups of motions, understood both as groups with a unary predicate singling out line-reflections, and as groups acting on sets, are mutually inter-pretable.

Original languageEnglish (US)
Pages (from-to)387-398
Number of pages12
JournalStudia Logica
Volume81
Issue number3
DOIs
StatePublished - Dec 2005

Fingerprint

First-order
Unary
Predicate
Motion
Line
Geometry
Onset
Class

Keywords

  • Erlanger Programm
  • Group actions
  • Groups generated by involutions
  • Line reflections
  • Metric planes
  • Mutually interpretable theories

ASJC Scopus subject areas

  • Logic

Cite this

Groups and plane geometry. / Pambuccian, Victor.

In: Studia Logica, Vol. 81, No. 3, 12.2005, p. 387-398.

Research output: Contribution to journalArticle

Pambuccian, Victor. / Groups and plane geometry. In: Studia Logica. 2005 ; Vol. 81, No. 3. pp. 387-398.
@article{cffaea136b37474f96e460cc8feef14a,
title = "Groups and plane geometry",
abstract = "We show that the first-order theory of a large class of plane geometries and the first-order theory of their groups of motions, understood both as groups with a unary predicate singling out line-reflections, and as groups acting on sets, are mutually inter-pretable.",
keywords = "Erlanger Programm, Group actions, Groups generated by involutions, Line reflections, Metric planes, Mutually interpretable theories",
author = "Victor Pambuccian",
year = "2005",
month = "12",
doi = "10.1007/s11225-005-4650-z",
language = "English (US)",
volume = "81",
pages = "387--398",
journal = "Studia Logica",
issn = "0039-3215",
publisher = "Springer Netherlands",
number = "3",

}

TY - JOUR

T1 - Groups and plane geometry

AU - Pambuccian, Victor

PY - 2005/12

Y1 - 2005/12

N2 - We show that the first-order theory of a large class of plane geometries and the first-order theory of their groups of motions, understood both as groups with a unary predicate singling out line-reflections, and as groups acting on sets, are mutually inter-pretable.

AB - We show that the first-order theory of a large class of plane geometries and the first-order theory of their groups of motions, understood both as groups with a unary predicate singling out line-reflections, and as groups acting on sets, are mutually inter-pretable.

KW - Erlanger Programm

KW - Group actions

KW - Groups generated by involutions

KW - Line reflections

KW - Metric planes

KW - Mutually interpretable theories

UR - http://www.scopus.com/inward/record.url?scp=28144462736&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=28144462736&partnerID=8YFLogxK

U2 - 10.1007/s11225-005-4650-z

DO - 10.1007/s11225-005-4650-z

M3 - Article

AN - SCOPUS:28144462736

VL - 81

SP - 387

EP - 398

JO - Studia Logica

JF - Studia Logica

SN - 0039-3215

IS - 3

ER -