Bulletin of the American Mathematical Society

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Book Information:

Author: J. L. Bell
Title: Toposes and local set theories: An introduction
Additional book information: Oxford Logic Guides: 14, Clarendon Press, Oxford, 1988, xii + 267 pp., $75.00. ISBN 0-19-853274-1.

M. Artin et al. (eds. ), Théorie des topos et cohomologie étale des schémas, Lecture Notes in Math., vol. 269, Springer-Verlag, Berlin and New York, 1972.

Michael Barr, Toposes without points, J. Pure Appl. Algebra 5 (1974), 265–280. MR 409602, DOI 10.1016/0022-4049(74)90037-1

André Boileau and André Joyal, La logique des topos, J. Symbolic Logic 46 (1981), no. 1, 6–16 (French). MR 604873, DOI 10.2307/2273251

Alonzo Church, A formulation of the simple theory of types, J. Symbolic Logic 5 (1940), 56–68. MR 1931, DOI 10.2307/2266170

Samuel Eilenberg and Saunders MacLane, General theory of natural equivalences, Trans. Amer. Math. Soc. 58 (1945), 231–294. MR 13131, DOI 10.1090/S0002-9947-1945-0013131-6

P. Freyd, On proving that 1 is an indecomposable projective in various free categories, manuscript 1978.

Kurt Gödel, Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I, Monatsh. Math. Phys. 38 (1931), no. 1, 173–198 (German). MR 1549910, DOI 10.1007/BF01700692

Théorie des topos et cohomologie étale des schémas. Tome 2, Lecture Notes in Mathematics, Vol. 270, Springer-Verlag, Berlin-New York, 1972 (French). Séminaire de Géométrie Algébrique du Bois-Marie 1963–1964 (SGA 4); Dirigé par M. Artin, A. Grothendieck et J. L. Verdier. Avec la collaboration de N. Bourbaki, P. Deligne et B. Saint-Donat. MR 0354653

Leon Henkin, Completeness in the theory of types, J. Symbolic Logic 15 (1950), 81–91. MR 36188, DOI 10.2307/2266967

P. T. Johnstone, Topos theory, London Mathematical Society Monographs, Vol. 10, Academic Press [Harcourt Brace Jovanovich, Publishers], London-New York, 1977. MR 0470019

Saul A. Kripke, Semantical analysis of intuitionistic logic. I, Formal Systems and Recursive Functions (Proc. Eighth Logic Colloq., Oxford, 1963) North-Holland, Amsterdam, 1965, pp. 92–130. MR 0201300

Joachim Lambek, From types to sets, Adv. in Math. 36 (1980), no. 2, 113–164. MR 574645, DOI 10.1016/0001-8708(80)90013-4

J. Lambek, On the unity of algebra and logic, Categorical algebra and its applications (Louvain-La-Neuve, 1987) Lecture Notes in Math., vol. 1348, Springer, Berlin, 1988, pp. 221–229. MR 975972, DOI 10.1007/BFb0081361

J. Lambek and P. J. Scott, Intuitionist type theory and the free topos, J. Pure Appl. Algebra 19 (1980), 215–257. MR 593255, DOI 10.1016/0022-4049(80)90102-4

J. Lambek and P. J. Scott, New proofs of some intuitionistic principles, Z. Math. Logik Grundlag. Math. 29 (1983), no. 6, 493–504. MR 723655, DOI 10.1002/malq.19830291004

J. Lambek and P. J. Scott, Introduction to higher order categorical logic, Cambridge Studies in Advanced Mathematics, vol. 7, Cambridge University Press, Cambridge, 1986. MR 856915

F. William Lawvere, An elementary theory of the category of sets, Proc. Nat. Acad. Sci. U.S.A. 52 (1964), 1506–1511. MR 172807, DOI 10.1073/pnas.52.6.1506

F. William Lawvere, Introduction, Toposes, algebraic geometry and logic (Conf., Dalhousie Univ., Halifax, N.S., 1971) Lecture Notes in Math., Vol. 274, Springer, Berlin, 1972, pp. 1–12. MR 0376798

F. William Lawvere, Variable quantities and variable structures in topoi, Algebra, topology, and category theory (a collection of papers in honor of Samuel Eilenberg), Academic Press, New York, 1976, pp. 101–131. MR 0419232

F. William Lawvere, Introduction, Model theory and topoi, Lecture Notes in Math., Vol. 445, Springer, Berlin, 1975, pp. 3–14. MR 0376807

Michael Makkai and Gonzalo E. Reyes, First order categorical logic, Lecture Notes in Mathematics, Vol. 611, Springer-Verlag, Berlin-New York, 1977. Model-theoretical methods in the theory of topoi and related categories. MR 0505486

William Mitchell, Boolean topoi and the theory of sets, J. Pure Appl. Algebra 2 (1972), 261–274. MR 319757, DOI 10.1016/0022-4049(72)90006-0

B. Russell and A. N. Whitehead, Principia Mathematica I-III, Cambridge Univ. Press, pp. 1910-1913.

Myles Tierney, Sheaf theory and the continuum hypothesis, Toposes, algebraic geometry and logic (Conf., Dalhousie Univ., Halifax, N.S., 1971) Lecture Notes in Math., Vol. 274, Springer, Berlin, 1972, pp. 13–42. MR 0373888

Hugo Volger, Logical categories, semantical categories and topoi, Model theory and topoi, Lecture Notes in Math., Vol. 445, Springer, Berlin, 1975, pp. 87–100. MR 0376809

M. Artin et al. (eds. ), Théorie des topos et cohomologie étale des schémas, Lecture Notes in Math., vol. 269, Springer-Verlag, Berlin and New York, 1972.




M. Barr, Toposes without points, J. Pure Appl. Algebra 5 (1974), 265-280. MR 0409602




A. Boileau and A. Joyal, La logique des topos, J. Symbolic Logic 46 (1981), 6-16. MR 604873




A. Church, A foundation of the simple theory of types, J. Symbolic Logic 5 (1940), 56-88. MR 1931




S. Eilenberg and S. Mac Lane, General theory of natural equivalences, Trans. Amer. Math. Soc. 58 (1945), 231-294. MR 13131




P. Freyd, On proving that 1 is an indecomposable projective in various free categories, manuscript 1978.




K. Gödel, Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, J. Monatsh. Math. Phys. 38 (1931), 173-198. MR 1549910




A. Grothendieck and J. L. Verdier, Topos, Artin et al. (eds. ) Lecture Notes in Math., vol. 269, Springer-Verlag, Berlin and New York, 1972, 229-515. MR 354653




L. A. Henkin, Completeness in the theory of types, J. Symbolic Logic 15 (1950), 81-91. MR 36188




P. T. Johnstone, Topos theory, London Mathematical Society Monographs, vol. 10, Academic Press, London 1977. MR 470019




S. A. Kripke, Semantic analysis of intuitionistic logic, I, J. N. Crossley et al. (eds.), Formal Systems and Recursive Functions, North-Holland Publ. Co., Amsterdam, 1965. MR 201300




J. Lambek, From types to sets, Advances in Math. 36 (1980), 113-164. MR 574645




J. Lambek, On the unity of algebra and logic, F. Borceux (ed.), Categorical Algebra and its Applications, Lecture Notes in Math., vol. 1348, Springer-Verlag, Berlin and New York, 1988, pp. 221-229. MR 975972




J. Lambek and P. J. Scott, Intuitionistic type theory and the free topos, J. Pure Appl. Algebra 19 (1980), 215-257. MR 593255




J. Lambek and P. J. Scott, New proofs of some intuitionistic principles, Z. Math. Logik Grundlag. Math. 29 (1983), 493-504. MR 723655




J. Lambek and P. J. Scott, Introduction to higher order categorical logic, Cambridge, Univ. Press, 1986. MR 856915




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




F. W. Lawvere, Introduction to toposes, algebraic geometry and logic, Lecture Notes in Math., vol. 274, Springer-Verlag, Berlin and New York, 1972, pp. 1-12. MR 376798




F. W. Lawvere, Variable quantities and variable structures in topoi, A. Heller et al. (eds.), Algebra, Topology and Category Theory, Academic Press, 1976, pp. 101-131. MR 419232




F. W. Lawvere et al. (eds.), Model theory and topoi, Lecture Notes in Math., vol. 445, Springer-Verlag, Berlin and New York, 1975. MR 376807




M. Makkai and G. E. Reyes, First order categorical logic, Lecture Notes in Math., vol. 661, Springer-Verlag, Berlin and New York, 1977. MR 505486




W. Mitchell, Boolean topoi and the theory of sets, J. Pure Appl. Algebra 2 (1972), 261-274. MR 319757




B. Russell and A. N. Whitehead, Principia Mathematica I-III, Cambridge Univ. Press, pp. 1910-1913.




M. Tierney, Sheaf theory and the continuum hypothesis, Toposes, Algebraic Geometry and Logic, F. W. Lawvere (ed.), Lecture Notes in Math., vol. 274, Springer-Verlag, Berlin and New York, 1972, pp. 13-42. MR 373888




H. Volger, Logical categories, semantical categories and topoi, Model Theory and Topoi, F. W. Lawvere et al. (eds.), Springer-Verlag, Berlin and New York, 1975, pp. 87-100. MR 376809