Sequent calculus proof theory of intuitionistic apartness and order relations

Archive for Mathematical Logic

Volumn 38, Issue 8, 1999, Pages 521-547

  Negri, Sara ^a  

^a UNIVERSITY OF HELSINKI   (Finland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038702395     PISSN: 09335846     EISSN: None     Source Type: Journal    
DOI: 10.1007/s001530050137     Document Type: Article

References (16)

1. J. Cederquist, T. Coquand, S. Negri. The Hahn-Banach theorem in type theory, in G. Sambin and J. Smith (eds), Twenty-Five Years of Constructive Type Theory, pp. 39-50, Oxford University Press, 1998.
2. D. van Dalen, R. Statman. Equality in the presence of apartness, in J. Hintikka et al. (eds), Essays in Mathematical and Philosophical Logic, pp. 95-116, Reidel, Dordrecht, 1979.
3. A. Dragalin. Mathematical Intuitionism. An Introduction to Proof Theory, American Mathematical Society, Providence, Rhode Island, 1988. Russian original 1979.
4. R. Dyckhoff. Contraction-free sequent calculi for intuitionistic logic, The Journal of Symbolic Logic, vol. 57, pp. 795-807, 1992.
5. R. Dyckhoff. Dragalin's proofs of cut-admissibility for the intuitionistic sequent calculi G3i and G3i′, Research Report CS/97/8, Computer Science Division, St Andrews University, 1997, available from "http://www-theory.dcs.stand.ac.uk/~rd/publications/".
6. R. Dyckhoff, S. Negri. Admissibility of structural rules in contraction-free systems for intuitionistic logic, The Journal of Symbolic Logic, in press.
7. R. Dyckhoff, S. Negri. Admissibility of structural rules in extensions of contraction-free systems for intuitionistic logic, forthcoming.
8. G. Gentzen. New version of the consistency proof for elementary number theory, in M.E. Szabo ed., The Collected Papers of Gerhard Gentzen, North-Holland, pp. 252-277, 1969.
9. J. Hudelmaier. Bounds for cut elimination in intuitionistic propositional logic, Archive for Mathematical Logic, vol. 31, pp. 331-354, 1992.
10. S. Kleene. Permutability of inferences in Gentzen's calculi LK and LJ, Memoirs of the American Mathematical Society, vol. 10, pp. 1-26, 1952.
11. S. Kleene. Introduction to Metamathematics, North-Holland, Amsterdam, 1952.
12. S. Negri, J. von Plato. From Kripke Models to Algebraic Counter-valuations, in H. de Swart ed., Theorem Proving with Analytic Tableaux and Related Methods, Lecture Notes in Artificial Intelligence 1397, Springer Verlag, pp. 247-261, 1998.
13. J. von Plato. Positive Heyting algebras, manuscript, 1997.
14. D. Scott. Extending the topological interpretation to intuitionistic analysis, Compositio Mathematica, vol. 20, pp. 194-210, 1968.
15. C. Smorynski. On axiomatizing fragments, The Journal of Symbolic Logic, vol. 42, pp. 530-540, 1977.
16. A.S. Troelstra, H. Schwichtenberg. Basic Proof Theory, Cambridge University Press, 1996.