Constructive projective extension of an incidence plane

Mandelkern, Mark

doi:10.1090/S0002-9947-2013-05880-1

Constructive projective extension of an incidence plane
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Trans. Amer. Math. Soc. 366 (2014), 691-706 Request permission

Abstract:

A standard procedure in classical projective geometry, using pencils of lines to extend an incidence plane to a projective plane, is examined from a constructive viewpoint. Brouwerian counterexamples reveal the limitations of traditional pencils. Generalized definitions are adopted to construct a projective extension. The main axioms of projective geometry are verified. The methods used are in accordance with Bishop-type modern constructivism.

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