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Another Constructive Axiomatization of Euclidean Planes

โœ Scribed by Victor Pambuccian


Publisher
John Wiley and Sons
Year
2000
Tongue
English
Weight
158 KB
Volume
46
Category
Article
ISSN
0044-3050

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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,

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Bounded an unbounded Hilbert space V -Representations of the q-deformed Lie algebra of the group of plan motions are studied for different choices of involutions. Integrable (``well-behaved'') representations of the corresponding V -algebras are defined and described up to unitary equivalence. In th

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A quasimultiple affine plane of order \(n\) and multiplicity \(\lambda\) is a \((v, k, \lambda)=\left(n^{2}, n, \lambda\right)\) balanced incomplete block design. For those cases where the Bruck-Ryser theorem rules out \(\lambda=1\) it is an interesting problem to determine the smallest actual value