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Universal projective geometry via topos theory. (English) Zbl 0375.02016


MSC:

03F55 Intuitionistic mathematics
51E20 Combinatorial structures in finite projective spaces
18A15 Foundations, relations to logic and deductive systems
18B99 Special categories
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References:

[1] Artin, M.; Grothendieck, A.; Verdier, J. L., Théorie des topos et cohomologies étale des schemas (SGA 4), Springer Lecture Notes, Vol. 269 (1973)
[2] Bourbaki, N., Algébre. Ch., III (1970), Paris · Zbl 0211.02401
[3] Coste, M., Logique du \(l^{er}\) ordre dans les topos elementaire, Seminaire Benabou (1973-1974)
[4] Hakim, M., Topos anneles et schemas relatifs (1972), Springer Verlag · Zbl 0246.14004
[5] Heyting, A., Zur intuitionistischen Axiomatik der projektiven Geometrie, Math. Annal., 98, 491-538 (1928) · JFM 53.0541.01
[6] Klein, F., Höhere Geometrie (1926), Springer Verlag · JFM 52.0624.09
[7] Kock, A., Linear algebra and projective geometry in the Zariski topos (1974/75), Aarhus Universitet, No. 4.
[8] Kock, A., Linear algebra in a local ringed site, Communications in Algebra, 3, 545-561 (1975) · Zbl 0308.18002
[9] Kock, A.; Lecouturier, P.; Mikkelsen, C. J.; Lawvere, F. W., Some topos-theoretic concepts of finiteness, Springer Lecture Notes, Vol. 445 (1975) · Zbl 0334.18010
[10] Makkai, M.; Reyes, G., Model theoretic methods in the theory of topoi and related categories, I, II (1974), (to appear in book form).
[11] Mulvey, C.; Hofmann, K. H., Non-standard algebra and representations of rings, Mem. A.M.S., 148 (1974)
[12] Oullet, R., Axiomatisation de la logique du premier ordre des topos, version inclusive et multisorte, (Thèse (1974), Université de Montréal)
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