TERNARY OPERATIONS AS PRIMITIVE NOTIONS FOR PLANE GEOMETRY II

Victor Pambuccian

doi:10.1002/malq.19920380132

TERNARY OPERATIONS AS PRIMITIVE NOTIONS FOR PLANE GEOMETRY II

Victor Pambuccian

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

9 Scopus citations

Abstract

We proved in the first part [1] that plane geometry over Pythagorean fields is axiomatizable by quantifier‐free axioms in a language with three individual constants, one binary and three ternary operation symbols. In this paper we prove that two of these operation symbols are superfluous.

Original language	English (US)
Pages (from-to)	345-348
Number of pages	4
Journal	Mathematical Logic Quarterly
Volume	38
Issue number	1
DOIs	https://doi.org/10.1002/malq.19920380132
State	Published - 1992
Externally published	Yes

Keywords

Foundations of plane geometry
axiomatization of plane geometry
definability in geometry

ASJC Scopus subject areas

Logic

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10.1002/malq.19920380132

Cite this

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title = "TERNARY OPERATIONS AS PRIMITIVE NOTIONS FOR PLANE GEOMETRY II",

abstract = "We proved in the first part [1] that plane geometry over Pythagorean fields is axiomatizable by quantifier‐free axioms in a language with three individual constants, one binary and three ternary operation symbols. In this paper we prove that two of these operation symbols are superfluous.",

keywords = "Foundations of plane geometry, axiomatization of plane geometry, definability in geometry",

author = "Victor Pambuccian",

year = "1992",

doi = "10.1002/malq.19920380132",

language = "English (US)",

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pages = "345--348",

journal = "Mathematical Logic Quarterly",

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AB - We proved in the first part [1] that plane geometry over Pythagorean fields is axiomatizable by quantifier‐free axioms in a language with three individual constants, one binary and three ternary operation symbols. In this paper we prove that two of these operation symbols are superfluous.

KW - Foundations of plane geometry

KW - axiomatization of plane geometry

KW - definability in geometry

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ER -

TERNARY OPERATIONS AS PRIMITIVE NOTIONS FOR PLANE GEOMETRY II

Abstract

Keywords

ASJC Scopus subject areas

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