CONSTRUCTIVE PROJECTIVE EXTENSION OF AN INCIDENCE PLANE

被引：0

作者：

Mandelkern, Mark ^{[1
]}

机构：

[1] New Mexico State Univ, Dept Math, Las Cruces, NM 88003 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2014年 / 366卷 / 02期

关键词：

Projective extension; incidence plane; constructive mathematics;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：691 / 706

页数：16

共 17 条

[1]

[Anonymous], 1985, Math. Mag.

[2] FOUNDATIONS OF INTUITIONISTIC MATHEMATICS [J].

BISHOP, E .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1965, 71 (06) :850-&

[3]

Bishop E., 1985, CONSTRUCTIVE ANAL

[4]

Bishop E., 1967, FDN CONSTRUCTIVE ANA

[5]

Bridges D., 1987, VARIETIES CONSTRUCTI

[6]

Brouwer L. E. J., 1908, Tijdschrift Wijsbegeerte, V2, P152

[7]

Heyting A., 1959, AXIOMATIC METHOD, P160, DOI [10.1016/S0049-237X(09)70026-6, DOI 10.1016/S0049-237X(09)70026-6]

[8] LIMITED OMNISCIENCE AND THE BOLZANO-WEIERSTRASS PRINCIPLE [J].

MANDELKERN, M .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1988, 20 :319-320

[9]

Mandelkern M., 1983, MEM AM MATH SOC, V42

[10]

Mandelkern M., 2007, BEITRAGE ALGEBRA GEO, V48, P547

← 1 2 →