Topological representation of the 2-calculus

Mathematical Structures in Computer Science

Volumn 10, Issue 1, 2000, Pages 81-

  Awodey, Steven ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 80355146596     PISSN: 09601295     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0960129599002972     Document Type: Article

References (20)

1. Awodey, S. and Butz, C. (1997) Topological completeness for higher-order logic. Tech. Report RS-97-21, BRICS, Aahrus University, Denmark. (Forthcoming in the Journal of Symbolic Logic.)
2. Barendregt, H. (1984) The lambda calculus, its syntax and semantics, North-Holland.
3. Butz, C. (1996) Logical and cohomological aspects of the space of points of a topos, Ph. D. thesis, Universiteit Utrecht.
4. Butz, C. and Johnstone, P. (1998) Classifying toposes for first-order theories. Annals of Pure and Applied Logic 91 33–58.
5. Butz, C. and Moerdijk, I. (1996) Topological representation of sheaf cohomology of sites. Tech. Report 973, Universiteit Utrecht.
6. Church, A. (1940) A foundation for the simple theory of types. Journal of Symbolic Logic 5 56–68.
7. Cubrić, D. (1998) Embedding a free cartesian closed category into the category of sets. Journal of Pure and Applied Algebra 126 121–147.
8. Freyd, P. (1964) Abelian categories: An introduction to the theory of functors, Harper and Row.
9. Friedman, H. (1975) Equality between functionals. In: Parikh, R. (ed.) Logic Colloquium 73, Springer-Verlag.
10. Henkin, L. (1950) Completeness in the theory of types. Journal of Symbolic Logic 15 81–91.
11. Joyal, A. and Moerdijk, I. (1990) Toposes as homotopy groupoids. Advances in Mathematics 80 22–38.
12. Lambek, J. and Scott, P. J. (1986) Introduction to higher-order categorical logic, Cambridge University Press.
13. Mac Lane, S. and Moerdijk, I. (1992) Sheaves in geometry and logic: A first introduction to topos theory, Springer-Verlag.
14. Mitchell, J. and Moggi, E. (1991) Kripke-style models for typed lambda calculus. Annals of Pure and Applied Logic 51 99–124.
15. Mitchell, J. and Scott, P. (1988) Typed lambda models and cartesian closed categories. Contemporary Mathematics 92 301–316.
16. Moerdijk, I. and Palmgren, E. (1999) Wellfounded trees in categories (unpublished manuscript).
17. Pitts, A. (1995) Categorical logic. In: Abramsky, A. et al. (eds.) Handbook of Logic in Computer Science, vol. 6, Oxford University Press (forthcoming).
18. Scott, D. (1980) Relating theories of the lambda calculus. In: (eds.) To H.B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, Academic Press 403–450.
19. Seely, R. (1984) Locally cartesian closed categories and type theory. Mathematical Proceedings of the Cambridge Philosophical Society 95 33–48.
20. Simpson, A. (1996) Categorical completeness results for the simply-typed lambda-calculus. Typed Lambda Calculi and Applications, Proceedings of TLCA ’95. Springer-Verlag Lecture Notes in Computer Science 902 414–427.