Logique, catégories et faisceaux
Séminaire Bourbaki (1977-1978)
- Volume: 20, page 123-146
- ISSN: 0303-1179
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topCartier, Pierre. "Logique, catégories et faisceaux." Séminaire Bourbaki 20 (1977-1978): 123-146. <http://eudml.org/doc/109913>.
@article{Cartier1977-1978,
author = {Cartier, Pierre},
journal = {Séminaire Bourbaki},
keywords = {Generalized ContinuUm Hypothesis; Historical Survey; Mathematical Logic; Heyting Algebras; Topoi; Sheaves; Intuitionistic Logic; Categorical Logic; Independence},
language = {fre},
pages = {123-146},
publisher = {Springer-Verlag},
title = {Logique, catégories et faisceaux},
url = {http://eudml.org/doc/109913},
volume = {20},
year = {1977-1978},
}
TY - JOUR
AU - Cartier, Pierre
TI - Logique, catégories et faisceaux
JO - Séminaire Bourbaki
PY - 1977-1978
PB - Springer-Verlag
VL - 20
SP - 123
EP - 146
LA - fre
KW - Generalized ContinuUm Hypothesis; Historical Survey; Mathematical Logic; Heyting Algebras; Topoi; Sheaves; Intuitionistic Logic; Categorical Logic; Independence
UR - http://eudml.org/doc/109913
ER -
References
top- [1] F.W. Lawvere - An elementary theory of the category of sets , Proc. Nat. Acad. Sci. U.S.A., 52(1964) , p. 1506-1511. Zbl0141.00603MR172807
- [2] ---- An elementary theory of the category of sets , notes polycopiées , 43 pages , Université de Chicago , 1964. MR396262
- [3] ---- Adjointness in foundations , Dialectica, 23(1969) , p. 281-296. Zbl0341.18002
- [4] ---- Equality in hyperdoctrines and comprehension schema as an adjoint functor , Symposia Pure Maths., vol. XVII , Amer. Math. Soc. , 1970 , p. 1-14. Zbl0234.18002MR257175
- [5] ---- Quantifiers and sheaves , Actes du CongrèsIntern. des Math., Nice , 1970 , vol. I , p. 329-334. Zbl0261.18010MR430021
- [6] ---- Continuously variable sets : algebraic geometry = geometric logic , in Bristol Logic Colloquium '73 , North Holland , 1975 , p. 135-156. Zbl0364.18002MR392567
- [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. Zbl0353.02043MR419232
- [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 , PrincetonUniversity Press , 1941. MR5274JFM67.0041.01
- [11] H. Curry , R. Feys et W. Craig - Combinatory Logic , vol. I , North Holland , 1958. Zbl0175.27601MR94298
- [12] G. Gentzen - Collected Papers (M. Szabo édit.) , North Holland , 1969. MR262050
- [13] J. van Heijenoort - Frege and Gödel (Two fundamental texts in mathematical logic), Harvard University Press , 1970. Zbl0209.00601MR263601
- [14] D. Hilbert et W. Ackermann - Grundzüge der theoretischen Logik , 5e édit. , Springer , 1967. Zbl0158.00602
- [15] S. Kleene - Introduction to Metamathematics , van Nostrand , 1952. Zbl0047.00703MR51790
- [16] Y. Manin - A course in Mathematical Logic , Springer , 1977. Zbl0383.03002MR457126
- [17] G. Birkhoff - Lattice theory , Colloquium Publ. , vol. XXV , 3e édit. , Amer. Math. Soc. , 1967. Zbl0153.02501MR227053
- [18] P. Halmos - Lectures on Boolean algebras , van Nostrand , 1963. Zbl0114.01603MR167440
- [19] A. Heyting - Intuitionism . An introduction , North Holland , 1956. Zbl0070.00801MR75147
- [20] J. McKinsey et A. Tarski - On closed elements in closure algebras , Ann. of Maths, 47(1946) , p. 122-162. Zbl0060.06207MR15037
- [21] R. Sikorski - Boolean algebras , Springer , 1964. Zbl0123.01303MR126393
- [22] H. Rasiowa et R. Sikorski - The mathematics of metamathematics , Monografie Mat. vol. 41 , Varsovie , 1963. Zbl0122.24311MR163850
- [23] M. Artin - Grothendieck topologies , notes polycopiées , Harvard, 1962. Zbl0208.48701
- [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. Zbl0234.00007MR354653
- [25] J. Giraud - Classifying topos , dans [8] , p. 43-56. Zbl0267.18014MR349807
- [26] ---- Analysis Situs [d'après Artin et Grothendieck] , Sém. Bourbaki1962/3 , exposé 256 , 11 pages , Benjamin , 1966.
- [27] M. Hakim - Topos annelés et schémas relatifs , Springer , 1972. Zbl0246.14004MR364245
- [28] R. Godement - Topologie algébrique et théorie des faisceaux , Hermann , 1958. Zbl0080.16201MR102797
- [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 . Zbl0252.18001
- [31] P. Johnstone - Topos theory , London Math. Soc. vol. 10 , Academic Press , 1977. Zbl0368.18001MR470019
- [32] A. Kock et C. Mikkelsen - Topos theoretic factorization of non-standard analysis, Lecture Notes in Maths., vol. 369 , Springer , 1974 , p. 122-143. Zbl0276.18001MR480685
- [33] A. Kock et G. Wraith - Elementary toposes , Aarhus Lecture Notes , vol. 30 , 1971. Zbl0251.18015MR342578
- [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. Zbl0268.18002MR354800
- [35] ---- Forcing topologies and classifying topoi , in Algebra , Topology and Category Theory (éd. A. Heller et M. Tierney) , Academic Press , 1976 , p. 211-219. Zbl0356.18012MR409605
- [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. Zbl0176.28901MR235979
- [39] W. Mitchell - Boolean topoi and the theory of sets , Journ. Pure and Applied Alg., 2(1972) , p. 261-274. Zbl0245.18001MR319757
- [40] G. Osius - Logical and set theoretical tools in elementary topoi , in [9] , p. 297-346. Zbl0348.18002MR387050
- [41] ---- A note on Kripke-Joyal semantics for the internal language of topoi , in [9] , p. 349-354. MR387051
- [42] H. Volger - Logical categories , semantical categories and topoi , in [9] , p. 87-100. Zbl0338.18002MR376809
- [43] P. Bernays et A. Fraenkel - Axiomatic set theory , North Holland , 1968. Zbl0175.27002MR252214
- [44] P. Cohen - Set theory and the continuum hypothesis , Benjamin , 1966. Zbl0182.01301MR232676
- [45] K. Godel - The consistency of the axiom of choice and the generalized continuum-hypothesis with the axioms of set theory , 4e édit. , PrincetonUniversity Press , 1958. JFM64.0035.01
- [46] R. Jensen - Modelle der Mengenlehre , Lecture Notes in Maths., vol. 37 , Springer , 1967. Zbl0191.29901MR221930
- [47] A. Mostowski - An undecidable arithmetical statement , Fund. Math., 36(1949) , p. 143-164. Zbl0039.00802MR35721
- [48] J. Rosser - Simplified independence proofs (Boolean valued models of set theory), Academic Press , 1969. Zbl0209.30502MR249290
- [49] P. Samuel - Modèles booléiens et hypothèse du continu , Sém. Bourbaki1966/7 , exposé 317 , 12 pages , Benjamin , 1968. Zbl0197.00401
- [50] D. Scott - A proof of the independence of the continuum hypothesis , Math. Systems Theory , 1(1967) , p. 89-111. Zbl0149.25302MR218233
- [51] J. Cole - Categories of sets and models of set theory , Proc. Bertrand Russell Memorial Logic Conference , Uldum1971 , Leeds1973 , p. 351-399. MR357116
- [52] G. Osius - Categorical set theory : a characterization of the category of sets , Journ. Pure and Applied Alg., 4(1974) , p. 79-119. Zbl0282.02027MR364389
- [53] M. Tierney - Sheaf theory and the continuum hypothesis , in [8] , p. 13-42. Zbl0244.18005MR373888
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