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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Self-dual axioms for many-dimensional projective geometry


Author: Martinus Esser
Journal: Trans. Amer. Math. Soc. 177 (1973), 221-236
MSC: Primary 50A20
DOI: https://doi.org/10.1090/S0002-9947-1973-0320871-5
MathSciNet review: 0320871
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Abstract: Proposed and compared are four equivalent sets R, S, T, D of self-dual axioms for projective geometries, using points, hyperplanes and incidence as primitive elements and relation. The set R is inductive on the number of dimensions. The sets S, T, D all include the axiom ``on every n points there is a plane", the dual of this axiom, one axiom on the existence of a certain configuration, and one or several axioms on the impossibility of certain configurations. These configurations consist of $ (n + 1)$ points and $ (n + 1)$ planes for sets S, T, but of $ (n + 2)$ points and $ (n + 2)$ planes for set D. Partial results are obtained by a preliminary study of self-dual axioms for simplicial spaces (spaces which may have fewer than 3 points per line).


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DOI: https://doi.org/10.1090/S0002-9947-1973-0320871-5
Keywords: Projective, geometry, axioms, designs (or blocks), foundations
Article copyright: © Copyright 1973 American Mathematical Society