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On the foundations of incidence geometry
Geometriae Dedicata, 1988The tremendous and sudden development of diagram geometries and related concepts such as chamber systems, combinatorial maps, incidence complexes (see for instance [2], [14], [15], [3]) and their application to finite group theory (see [1], [11], [12]) justifies a careful study of the foundations of the subject, somewhat in the spirit of abstract ...
Buekenhout, Francis, Buset, Dominique
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The complexity of plane hyperbolic incidence geometry is ????
MLQ, 2005We show that plane hyperbolic geometry, expressed in terms of points and the ternary relation of collinearity alone, cannot be expressed by means of axioms of complexity at most ∀∃∀, but that there is an axiom system, all of whose axioms are ∀∃∀∃ sentences. This remains true for Klingenberg's generalized hyperbolic planes, with arbitrary ordered fields
V. Pambuccian
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Modal logics for incidence geometries
Journal of Logic and Computation, 1997International audience ; Incidence geometry is based on two-sorted structures consisting of ‘points’ and ‘lines’ together with an intersort binary relation called incidence. We introduce an equivalent one-sorted geometrical structure, called incidence frame, which is suitable for modal considerations. Incidence frames constitute the semantical basis of
Balbiani, Philippe +3 more
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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.
George D. Parker, Richard S. Millman
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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.
George D. Parker, Richard S. Millman
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on the incidence geometry of grassmann spaces
Geometriae Dedicata, 1999In this paper we identify some properties on the point-line structure of Grassmannians which are useful tools to characterize the incidence geometry of Grassmann varieties and of their special quotients.
FERRARA DENTICE, Eva, MELONE N.
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Left ventricular geometry and risk of incident hypertension [PDF]
Heart, 2019 ObjectiveLeft ventricular (LV) geometry change is an independent predictor for cardiovascular disease. However, data are equivocal on the association of echocardiographic parameters of LV geometry with incident hypertension. Thus, we were to investigate the risk of hypertension according to the baseline echocardiographic parameters of LV geometry ...
Sung Keun Park +4 more
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Two incidence propositions in chain geometries
Monatshefte für Mathematik, 2011The significance of the incidence propositions (Z) and (B) for chain geometries Σ(F, A, J) is determined. In preparation the structure of kinematic and nearquadratic Jordan systems is studied.
Münevver Özcan, Armin Herzer
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