Bulletin (New Series) of the American Mathematical Society

Review: J. L. Bell, Toposes and local set theories: An introduction

J. Lambek

Full-text: Open access

Article information

Source
Bull. Amer. Math. Soc. (N.S.) Volume 21, Number 2 (1989), 325-332.

Dates
First available in Project Euclid: 4 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.bams/1183555325

Citation

Lambek, J. Review: J. L. Bell, Toposes and local set theories: An introduction. Bull. Amer. Math. Soc. (N.S.) 21 (1989), no. 2, 325--332.https://projecteuclid.org/euclid.bams/1183555325


Export citation

References

  • 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.
  • A. Boileau and A. Joyal, La logique des topos, J. Symbolic Logic 46 (1981), 6-16.
  • A. Church, A foundation of the simple theory of types, J. Symbolic Logic 5 (1940), 56-88.
  • S. Eilenberg and S. Mac Lane, General theory of natural equivalences, Trans. Amer. Math. Soc. 58 (1945), 231-294.
  • 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.
  • 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.
  • L. A. Henkin, Completeness in the theory of types, J. Symbolic Logic 15 (1950), 81-91.
  • P. T. Johnstone, Topos theory, London Mathematical Society Monographs, vol. 10, Academic Press, London 1977.
  • 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.
  • J. Lambek, From types to sets, Advances in Math. 36 (1980), 113-164.
  • 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.
  • J. Lambek and P. J. Scott, Intuitionistic type theory and the free topos, J. Pure Appl. Algebra 19 (1980), 215-257.
  • J. Lambek and P. J. Scott, New proofs of some intuitionistic principles, Z. Math. Logik Grundlag. Math. 29 (1983), 493-504.
  • J. Lambek and P. J. Scott, Introduction to higher order categorical logic, Cambridge, Univ. Press, 1986.
  • F. W. Lawvere, An elementary theory of the category of sets, Proc. Nat. Acad. Sci. U. S. A. 52 (1964), 1506-1511.
  • 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.
  • 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.
  • F. W. Lawvere et al. (eds.), Model theory and topoi, Lecture Notes in Math., vol. 445, Springer-Verlag, Berlin and New York, 1975.
  • M. Makkai and G. E. Reyes, First order categorical logic, Lecture Notes in Math., vol. 661, Springer-Verlag, Berlin and New York, 1977.
  • W. Mitchell, Boolean topoi and the theory of sets, J. Pure Appl. Algebra 2 (1972), 261-274.
  • 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.
  • 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.