Positive definitions of segment congruence in terms of segment inequality

Victor Pambuccian

doi:10.1007/s00010-006-2844-8

Positive definitions of segment congruence in terms of segment inequality

Victor Pambuccian

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

2 Scopus citations

Abstract

It is shown that segment congruence can be defined by means of a positive existential definition in terms of segment inequality in several geometries over Archimedean ordered fields, and that it can be defined by means of a positive sentence in n-dimensional Euclidean geometry over arbitrary ordered fields.

Original language	English (US)
Pages (from-to)	243-253
Number of pages	11
Journal	Aequationes Mathematicae
Volume	72
Issue number	3
DOIs	https://doi.org/10.1007/s00010-006-2844-8
State	Published - Dec 2006

Keywords

Infinitary logic
Positive existential definability
Segment congruence
Segment inequality

ASJC Scopus subject areas

General Mathematics
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1007/s00010-006-2844-8

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title = "Positive definitions of segment congruence in terms of segment inequality",

abstract = "It is shown that segment congruence can be defined by means of a positive existential definition in terms of segment inequality in several geometries over Archimedean ordered fields, and that it can be defined by means of a positive sentence in n-dimensional Euclidean geometry over arbitrary ordered fields.",

keywords = "Infinitary logic, Positive existential definability, Segment congruence, Segment inequality",

author = "Victor Pambuccian",

year = "2006",

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KW - Infinitary logic

KW - Positive existential definability

KW - Segment congruence

KW - Segment inequality

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Positive definitions of segment congruence in terms of segment inequality

Abstract

Keywords

ASJC Scopus subject areas

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