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Constructive projective extension of an incidence plane


Author: Mark Mandelkern
Journal: Trans. Amer. Math. Soc. 366 (2014), 691-706
MSC (2010): Primary 51A45; Secondary 03F65
DOI: https://doi.org/10.1090/S0002-9947-2013-05880-1
Published electronically: August 8, 2013
MathSciNet review: 3130314
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Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

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Additional Information

Mark Mandelkern
Affiliation: Department of Mathematics, New Mexico State University, Las Cruces, New Mexico 88003
Email: mandelkern@member.ams.org

DOI: https://doi.org/10.1090/S0002-9947-2013-05880-1
Keywords: Projective extension, incidence plane, constructive mathematics
Received by editor(s): February 2, 2012
Published electronically: August 8, 2013
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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