Logique, catégories et faisceaux

Cartier, Pierre

Séminaire Bourbaki : vol. 1977/78, exposés 507-524, Séminaire Bourbaki, no. 20 (1979), Talk no. 513, p. 123-146

@incollection{SB_1977-1978__20__123_0,
     author = {Cartier, Pierre},
     title = {Logique, cat\'egories et faisceaux},
     booktitle = {S\'eminaire Bourbaki : vol. 1977/78, expos\'es 507-524},
     author = {Collectif},
     series = {S\'eminaire Bourbaki},
     publisher = {Springer-Verlag},
     number = {20},
     year = {1979},
     note = {talk:513},
     pages = {123-146},
     zbl = {0406.03074},
     mrnumber = {554218},
     language = {fr},
     url = {http://www.numdam.org/item/SB_1977-1978__20__123_0}
}

Cartier, Pierre. Logique, catégories et faisceaux, in Séminaire Bourbaki : vol. 1977/78, exposés 507-524, Séminaire Bourbaki, no. 20 (1979), Talk no. 513, pp. 123-146. http://www.numdam.org/item/SB_1977-1978__20__123_0/

References

[1] F.W. Lawvere - An elementary theory of the category of sets , Proc. Nat. Acad. Sci. U.S.A., 52(1964) , p. 1506-1511. | MR 172807 | Zbl 0141.00603

[2] ---- An elementary theory of the category of sets , notes polycopiées , 43 pages , Université de Chicago , 1964. | MR 396262

[3] ---- Adjointness in foundations , Dialectica, 23(1969) , p. 281-296.

[4] ---- Equality in hyperdoctrines and comprehension schema as an adjoint functor , Symposia Pure Maths., vol. XVII , Amer. Math. Soc. , 1970 , p. 1-14. | MR 257175 | Zbl 0234.18002

[5] ---- Quantifiers and sheaves , Actes du Congrès Intern. des Math., Nice , 1970 , vol. I , p. 329-334. | MR 430021 | Zbl 0261.18010

[6] ---- Continuously variable sets : algebraic geometry = geometric logic , in Bristol Logic Colloquium '73 , North Holland , 1975 , p. 135-156. | MR 392567 | Zbl 0364.18002

[7] ---- Variable quantities and variable structures in topoi , in Algebra , Topology and Category Theory (éd. A. Heller et M. Tierney) , Academic Press , 1976 , p. 101-131. | MR 419232 | Zbl 0353.02043

[8] Toposes , algebraic geometry and logic , Lecture Notes in Maths., vol.274 , Springer , 1972.

[9] Model theory and topoi , Lecture Notes in Maths., vol. 445 , Springer , 1975 . Voici maintenant quelques ouvrages de référence sur la logique mathématique :

[10] A. Church - The calculi of lambda conversion , Annals of Math. Studies , 6 , Princeton University Press , 1941. | JFM 67.0041.01 | MR 5274

[11] H. Curry , R. Feys et W. Craig - Combinatory Logic , vol. I , North Holland , 1958. | MR 94298 | Zbl 0175.27601

[12] G. Gentzen - Collected Papers (M. Szabo édit.) , North Holland , 1969. | MR 262050

[13] J. Van Heijenoort - Frege and Gödel (Two fundamental texts in mathematical logic), Harvard University Press , 1970. | MR 263601 | Zbl 0209.00601

[14] D. Hilbert et W. Ackermann - Grundzüge der theoretischen Logik , 5e édit. , Springer , 1967. | Zbl 0158.00602

[15] S. Kleene - Introduction to Metamathematics , van Nostrand , 1952. | MR 51790 | Zbl 0047.00703

[16] Y. Manin - A course in Mathematical Logic , Springer , 1977. | MR 457126 | Zbl 0383.03002

[17] G. Birkhoff - Lattice theory , Colloquium Publ. , vol. XXV , 3e édit. , Amer. Math. Soc. , 1967. | MR 227053 | Zbl 0153.02501

[18] P. Halmos - Lectures on Boolean algebras , van Nostrand , 1963. | MR 167440 | Zbl 0114.01603

[19] A. Heyting - Intuitionism . An introduction , North Holland , 1956. | MR 75147 | Zbl 0070.00801

[20] J. Mckinsey et A. Tarski - On closed elements in closure algebras , Ann. of Maths, 47(1946) , p. 122-162. | MR 15037 | Zbl 0060.06207

[21] R. Sikorski - Boolean algebras , Springer , 1964. | MR 126393 | Zbl 0123.01303

[22] H. Rasiowa et R. Sikorski - The mathematics of metamathematics , Monografie Mat. vol. 41 , Varsovie , 1963. | MR 163850 | Zbl 0122.24311

[23] M. Artin - Grothendieck topologies , notes polycopiées , Harvard, 1962. | Zbl 0208.48701

[24] M. Artin, A. Grothendieck et J.L. Verdier - Théorie des topos et cohomologie étale des schémas (SGA 4) , Lecture Notes in Maths., vol. 269 , Springer , 1972. | MR 354653

[25] J. Giraud - Classifying topos , dans [8] , p. 43-56. | MR 349807 | Zbl 0267.18014

[26] ---- Analysis Situs [d'après Artin et Grothendieck] , Sém. Bourbaki 1962/3 , exposé 256 , 11 pages , Benjamin , 1966.

[27] M. Hakim - Topos annelés et schémas relatifs , Springer , 1972. | MR 364245 | Zbl 0246.14004

[28] R. Godement - Topologie algébrique et théorie des faisceaux , Hermann , 1958. | MR 102797 | Zbl 0080.16201

[29] J. Bénabou et J. Celeyrette - Généralités sur les topos de Lawvere et Tierney , Sém. Bénabou , Université Paris-Nord , 1971.

[30] P. Freyd - Aspects of topoi , Bull. Austr. Math. Soc., 7(1972) , p. 1-76 et 467-480 . | Zbl 0252.18001

[31] P. Johnstone - Topos theory , London Math. Soc. vol. 10 , Academic Press , 1977. | MR 470019 | Zbl 0368.18001

[32] A. Kock et C. Mikkelsen - Topos theoretic factorization of non-standard analysis, Lecture Notes in Maths., vol. 369 , Springer , 1974 , p. 122-143. | MR 480685 | Zbl 0276.18001

[33] A. Kock et G. Wraith - Elementary toposes , Aarhus Lecture Notes , vol. 30 , 1971. | MR 342578 | Zbl 0251.18015

[34] M. Tierney - Axiomatic sheaf theory : some constructions and applications , in Categories and Commutative Algebra , C.I.M.E. III Ciclo 1971 , Edizioni Cremonese , 1973 , p. 249-326. | MR 354800 | Zbl 0268.18002

[35] ---- Forcing topologies and classifying topoi , in Algebra , Topology and Category Theory (éd. A. Heller et M. Tierney) , Academic Press , 1976 , p. 211-219. | MR 409605 | Zbl 0356.18012

[36] J. Bénabou - Catégories et logiques faibles , Journées sur les Catégories , Oberwolfach , 1973.

[37] M. Coste - Logique d'ordre supérieur dans les topos élémentaires , Sém. Bénabou , Université Paris-Nord , 1973/4.

[38] J. Lambek - Deductive systems and categories , I : Math. Systems Theory , 2(1968) , p. 287-318 ; II : Lecture Notes in Maths., vol.86 , Springer , 1969 , p. 76-122; III : in [8] , p. 57-82. | MR 235979 | Zbl 0176.28901

[39] W. Mitchell - Boolean topoi and the theory of sets , Journ. Pure and Applied Alg., 2(1972) , p. 261-274. | MR 319757 | Zbl 0245.18001

[40] G. Osius - Logical and set theoretical tools in elementary topoi , in [9] , p. 297-346. | MR 387050 | Zbl 0348.18002

[41] ---- A note on Kripke-Joyal semantics for the internal language of topoi , in [9] , p. 349-354. | MR 387051

[42] H. Volger - Logical categories , semantical categories and topoi , in [9] , p. 87-100. | MR 376809 | Zbl 0338.18002

[43] P. Bernays et A. Fraenkel - Axiomatic set theory , North Holland , 1968. | MR 252214 | Zbl 0175.27002

[44] P. Cohen - Set theory and the continuum hypothesis , Benjamin , 1966. | MR 232676 | Zbl 0182.01301

[45] K. Godel - The consistency of the axiom of choice and the generalized continuum-hypothesis with the axioms of set theory , 4e édit. , Princeton University Press , 1958. | JFM 64.0035.01

[46] R. Jensen - Modelle der Mengenlehre , Lecture Notes in Maths., vol. 37 , Springer , 1967. | MR 221930 | Zbl 0191.29901

[47] A. Mostowski - An undecidable arithmetical statement , Fund. Math., 36(1949) , p. 143-164. | MR 35721 | Zbl 0039.00802

[48] J. Rosser - Simplified independence proofs (Boolean valued models of set theory), Academic Press , 1969. | MR 249290 | Zbl 0209.30502

[49] P. Samuel - Modèles booléiens et hypothèse du continu , Sém. Bourbaki 1966/7 , exposé 317 , 12 pages , Benjamin , 1968. | Numdam | Zbl 0197.00401

[50] D. Scott - A proof of the independence of the continuum hypothesis , Math. Systems Theory , 1(1967) , p. 89-111. | MR 218233 | Zbl 0149.25302

[51] J. Cole - Categories of sets and models of set theory , Proc. Bertrand Russell Memorial Logic Conference , Uldum 1971 , Leeds 1973 , p. 351-399. | MR 357116

[52] G. Osius - Categorical set theory : a characterization of the category of sets , Journ. Pure and Applied Alg., 4(1974) , p. 79-119. | MR 364389 | Zbl 0282.02027

[53] M. Tierney - Sheaf theory and the continuum hypothesis , in [8] , p. 13-42. | MR 373888 | Zbl 0244.18005