Ternary Operations as Primitive Notions for Constructive Plane Geometry IV

Victor Pambuccian

doi:10.1002/malq.19940400111

Ternary Operations as Primitive Notions for Constructive Plane Geometry IV

Victor Pambuccian

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

11 Scopus citations

Abstract

In this paper we provide a quantifier‐free constructive axiomatization for Euclidean planes in a first‐order language with only ternary operation symbols and three constant symbols (to be interpreted as ‘points’). We also determine the algorithmic theories of some ‘naturally occurring’ plane geometries. Mathematics Subject Classification: 03F65, 51M05, 51M15, 03B30.

Original language	English (US)
Pages (from-to)	76-86
Number of pages	11
Journal	Mathematical Logic Quarterly
Volume	40
Issue number	1
DOIs	https://doi.org/10.1002/malq.19940400111
State	Published - 1994
Externally published	Yes

Keywords

Algorithmic logic
Constructive axiomatization
Euclidean planes

ASJC Scopus subject areas

Logic

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10.1002/malq.19940400111

Cite this

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title = "Ternary Operations as Primitive Notions for Constructive Plane Geometry IV",

abstract = "In this paper we provide a quantifier‐free constructive axiomatization for Euclidean planes in a first‐order language with only ternary operation symbols and three constant symbols (to be interpreted as {\textquoteleft}points{\textquoteright}). We also determine the algorithmic theories of some {\textquoteleft}naturally occurring{\textquoteright} plane geometries. Mathematics Subject Classification: 03F65, 51M05, 51M15, 03B30.",

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author = "Victor Pambuccian",

year = "1994",

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AB - In this paper we provide a quantifier‐free constructive axiomatization for Euclidean planes in a first‐order language with only ternary operation symbols and three constant symbols (to be interpreted as ‘points’). We also determine the algorithmic theories of some ‘naturally occurring’ plane geometries. Mathematics Subject Classification: 03F65, 51M05, 51M15, 03B30.

KW - Algorithmic logic

KW - Constructive axiomatization

KW - Euclidean planes

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Ternary Operations as Primitive Notions for Constructive Plane Geometry IV

Abstract

Keywords

ASJC Scopus subject areas

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