Results 261 to 270 of about 48,841 (303)

Modal logics for incidence geometries

Journal of Logic and Computation, 1997
Let \(S=(P,L,\text{in})\) be an incidence plane by the well-known axioms: \(P,L\neq\emptyset\); \(\text{in}\subseteq P\times L\); \(P\cap L=\emptyset\); two points are together incident with one and only one line; each line contains at least two different points; each point belongs at least to two different lines.
Philippe Balbiani, Luis Fariñas del Cerro, Tinko Tinchev, Dimiter Vakarelov   +3 more
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On the foundations of incidence geometry

Geometriae Dedicata, 1988
Diagram geometries and chamber systems of various types have been used and investigated intensively in recent years - not only in finite group theory, but in other areas as well. This development has led to a need for some clarification of the variations and generalizations introduced by the many authors, and for a discussion of the different axiomatic
Francis Buekenhout, Buekenhout Francis
exaly   +4 more sources

On finite models of Hilbert's incidence geometry

Discrete Mathematics
In this paper, the authors give a lower bound on the number of such models with \({n}\) points using finite models of the first group of Hilbert's axioms of Euclidean geometry (denote with \(A\)). By \(\mathrm{HilbInc}(n)\), the authors denote the number of nonisomorphic models of \(A\) with the point set \({1, 2,\dots,n}\) and calculate the exact ...
Kristina Ago, Bojan Basic
exaly   +4 more sources

Ordered Incidence geometry and the geometric foundations of convexity theory [PDF]

Journal of Geometry, 1987
An Ordered Incidence Geometry, that is a geometry with certain axioms of incidence and order, is proposed as a minimal setting for the fundamental convexity theorems, which usually appear in the context of a linear vector space, but require only ...
Ben-Tal Aharon
exaly   +2 more sources

An Introduction to Incidence Geometry

, 2016
This book gives an introduction to the field of Incidence Geometry by discussing the basic families of point-line geometries and introducing some of the mathematical techniques that are essential for their study.
De Bruyn, Bart, Bart De Bruyn, De Bruyn, Bart(ugent)801001184972(viaf)95252433   +2 more
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On the Incidence Geometry of Grassmann Spaces

Geometriae Dedicata, 1999
The main result is a characterization of the Grassmann space \({\mathbf G}\) of a projective space \(\mathcal P\). By definition, the point set \(P\) of \({\mathbf G}\) is the set of lines of \(\mathcal P\), the line set \(\mathcal L\) of \({\mathbf G}\) consists of all plane line pencils in \(\mathcal P\).
FERRARA DENTICE, Eva, MELONE N.
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FORMALIZATION OF HILBERT'S GEOMETRY OF INCIDENCE AND PARALLELISM

Synthese, 1997
The author first describes how \textit{D. Hilbert} changed the phrasing of his axioms of incidence in the various early editions of his Grundlagen der Geometrie [(Teubner, Leipzig) (1899; JFM 30.0424.01); second edition (1903; JFM 34.0523.01); seventh edition (1930; JFM 56.0481.01)], in which ``bestimmen'' gave way to ``es gibt''.
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Incidence and Metric Geometry

1981
In this section we shall define the notions of an abstract geometry and an incidence geometry. These are given by listing a set of axioms that must be satisfied. After the definitions are made, we will give a number of examples which will serve as models for these geometries.
Richard S. Millman, George D. Parker
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Geometric Hyperplanes of Lie Incidence Geometries

Geometriae Dedicata, 1997
Let \(\Gamma=({\mathcal P},{\mathcal L})\) be a geometry of points and lines. A subspace of \(\Gamma\) is a set of points which contains every line that meets it in at least two points. An embedding \(\mu\) of \(\Gamma\) in a finite-dimensional vector space \(V\) consists of a map \(\mu_1\) of \({\mathcal P}\) into the set of 1-subspaces of \(V\) and a
Cooperstein, Bruce N., Shult, Ernest E.
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