Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

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

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


Full text of review: PDF   This review is available free of charge.
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.
  • M. Barr, Toposes without points, J. Pure Appl. Algebra 5 (1974), 265-280. MR 409602
  • 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

Review Information:

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