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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Published electronically: August 8, 2013
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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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Additional Information

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

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05880-1
PII: S 0002-9947(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.