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Constructive Axiomatization of Plane Hyperbolic Geometry

✍ Scribed by Victor Pambuccian

Publisher: John Wiley and Sons
Year: 2001
Tongue: English
Weight: 202 KB
Volume: 47
Category: Article
ISSN: 0044-3050
DOI: 10.1002/1521-3870(200111)47:4<475::aid-malq475>3.0.co;2-s

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✦ Synopsis

We provide a universal axiom system for plane hyperbolic geometry in a firstorder language with two sorts of individual variables, 'points' (upper-case) and 'lines' (lowercase), containing three individual constants, A0, A1, A2, standing for three non-collinear points, two binary operation symbols, ϕ and ι, with ϕ(A, B) = l to be interpreted as 'l is the line joining A and B' (provided that A = B, an arbitrary line, otherwise), and ι(g, h) = P to be interpreted as 'P is the point of intersection of g and h (provided that g and h are distinct and have a point of intersection, an arbitrary point, otherwise), and two binary operation symbols, π1(P, l) and π2(P, l), with πi(P, l) = g (for i = 1, 2) to be interpreted as 'g is one of the two limiting parallel lines from P to l (provided that P is not on l, an arbitrary line, otherwise).

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