Extensional realizability

Annals of Pure and Applied Logic

Volumn 84, Issue 3, 1997, Pages 317-349

  Van Oosten, Jaap ^a  

^a UTRECHT UNIVERSITY   (Netherlands)

Author keywords

Extensional realizability; Intuitionistic arithmetic; Partial combinatory algebras; Realizability toposes

Indexed keywords

EID: 0031576983     PISSN: 01680072     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-0072(96)00050-4     Document Type: Article

References (24)

1. [1] P. Aczel, A note on interpreting higher order intuitionistic logic, manuscript, Manchester, 1980.
2. [2] M. Beeson, Recursive models of constructive set theories, Ann. Math. Logic 23 (1982) 127-178.
3. [3] M. Beeson, Foundations of Constructive Mathematics (Springer, Berlin, 1985).
4. [4] A. Carboni, Some free constructions in realizability and proof theory, Typeset manuscript, Milano, 1993; J. Pure Appl. Algebra 103 (1995) 117-148.
5. [4] A. Carboni, Some free constructions in realizability and proof theory, Typeset manuscript, Milano, 1993; J. Pure Appl. Algebra 103 (1995) 117-148.
6. [5] A. Carboni and R. Celia Magno, The free exact category on a left exact one, J. Australian Math. Soc. 33A (1982) 295-301.
7. [6] A. Carboni and E.M. Vitale, Completamento Esatto, manuscript, Louvain-la-Neuve, 1993.
8. [7] J. Diller and A.S. Troelstra, Realizability and intuitionistic logic, Synthese 60 (1984) 253-282.
9. [8] H. Friedman, On the derivability of instantiation properties, J. Symbolic Logic 42 (1977) 506-514.
10. [9] J.M.E. Hyland, The effective topos, in: A.S. Troelstra and D. Van Dalen, eds., The L.E.J. Brouwer Centenary Symposium, Studies in Logic, Amsterdam (1982) 165-216.
11. [10] J.M.E. Hyland, Realizability toposes, Talk given in Amsterdam, 1982 (Notes by A.S. Troelstra).
12. [11] J.M.E. Hyland, P.T. Johnstone and A.M. Pitts, Tripos Theory, Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 88 (1980) 205-232.
13. [12] P.T. Johnstone, Topos Theory (Academic Press, New York, 1977).
14. [13] A.M. Pitts, The theory of triposes, Ph.D. Thesis, Cambridge, 1981.
15. [14] S. MacLane and I. Moerdijk, Sheaves in Geometry and Logic (Springer, Berlin, 1992).
16. [15] G.R. Renardel de Lavalette, Extended bar induction in applicative theories, Ann. Pure Appl. Logic 50 (1990) 139-189.
17. [16] E. Robinson and G. Rosolini, Colimit completions and the effective topos, J. Symbolic Logic 55 (1990) 678-699.
18. [17] A.S. Troelstra, Notions of realizability for intuitionistic arithmetic and intuitionistic arithmetic in all finite types, in: J.E. Fenstad, ed., Proc. 2nd Scandinavian Logic Symposium (North-Holland, Amsterdam, 1971) 369-405.
19. [18] A.S. Troelstra, Metamathematical Investigations in Intuitionistic Arithmetic and Analysis, Lecture Notes in Math., Vol. 344 (Springer, Berlin, 1973).
20. [19] A.S. Troelstra, A note on non-extensional operations in connection with continuity and recursiveness, Proc. Koninklijke Nederlandse Academie van Wetenschappen, Vol. 80 (1977) 455-462.
21. [20] A.S. Troelstra and D. van Dalen, Constructivism in Mathematics (Elsevier, Amsterdam, 1988).
22. [21] E.M. Vitale, Left covering functors, Ph.D. Thesis, Louvain-la-Neuve, 1994.
23. [22] J. van Oosten, Lifschitz' realizability, J. Symbolic Logic 55 (1990) 805-821.
24. [23] J. van Oosten, Axiomatizing higher order Kleene realizability, Ann. Pure Appl. Logic 70 (1994) 87-111.