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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
[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, ()
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