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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

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Full text of review: PDF
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.

References [Enhancements On Off] (What's this?)

  • 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 0409602
  • André Boileau and André Joyal, La logique des topos, J. Symbolic Logic 46 (1981), no. 1, 6–16 (French). MR 604873, 10.2307/2273251
  • Alonzo Church, A formulation of the simple theory of types, J. Symbolic Logic 5 (1940), 56–68. MR 0001931
  • Samuel Eilenberg and Saunders MacLane, General theory of natural equivalences, Trans. Amer. Math. Soc. 58 (1945), 231–294. MR 0013131, 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, 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 0036188
  • P. T. Johnstone, Topos theory, Academic Press [Harcourt Brace Jovanovich, Publishers], London-New York, 1977. London Mathematical Society Monographs, Vol. 10. 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, 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, 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, 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, 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 0172807
  • F. William Lawvere, Introduction, Toposes, algebraic geometry and logic (Conf., Dalhousie Univ., Halifax, N.S., 1971) Springer, Berlin, 1972, pp. 1–12. Lecture Notes in Math., Vol. 274. 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, Springer, Berlin, 1975, pp. 3–14. Lecture Notes in Math., Vol. 445. 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 0319757
  • 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) Springer, Berlin, 1972, pp. 13–42. Lecture Notes in Math., Vol. 274. MR 0373888
  • Hugo Volger, Logical categories, semantical categories and topoi, Model theory and topoi, Springer, Berlin, 1975, pp. 87–100. Lecture Notes in Math., Vol. 445. MR 0376809

Review Information:

Reviewer: J. Lambek
Journal: Bull. Amer. Math. Soc. 21 (1989), 325-332
DOI: http://dx.doi.org/10.1090/S0273-0979-1989-15849-7