On the axiomatics of projective and affine geometry in terms of line intersection
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2013
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917586363482112 |
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| author | Havlicek, Hans Pambuccian, Victor |
| author_facet | Havlicek, Hans Pambuccian, Victor |
| contents | By providing explicit definitions, we show that in both affine and projective geometry of dimension $\geq 3$, considered as first-order theories axiomatized in terms of lines as the only variables, and the binary line-intersection predicate as primitive notion, non-intersection of two lines can be positively defined in terms of line-intersection. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1304_0224 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | On the axiomatics of projective and affine geometry in terms of line intersection Havlicek, Hans Pambuccian, Victor Algebraic Geometry Logic 51A05, 51A15, 03C40, 03B30 By providing explicit definitions, we show that in both affine and projective geometry of dimension $\geq 3$, considered as first-order theories axiomatized in terms of lines as the only variables, and the binary line-intersection predicate as primitive notion, non-intersection of two lines can be positively defined in terms of line-intersection. |
| title | On the axiomatics of projective and affine geometry in terms of line intersection |
| topic | Algebraic Geometry Logic 51A05, 51A15, 03C40, 03B30 |
| url | https://arxiv.org/abs/1304.0224 |