Groups and plane geometry

Victor Pambuccian

doi:10.1007/s11225-005-4650-z

Groups and plane geometry

Victor Pambuccian

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

11 Scopus citations

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 language	English (US)
Pages (from-to)	387-398
Number of pages	12
Journal	Studia Logica
Volume	81
Issue number	3
DOIs	https://doi.org/10.1007/s11225-005-4650-z
State	Published - Dec 1 2005

Keywords

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

ASJC Scopus subject areas

Logic
History and Philosophy of Science

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10.1007/s11225-005-4650-z

Cite this

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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",

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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

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ER -

Groups and plane geometry

Abstract

Keywords

ASJC Scopus subject areas

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