This is a preview of subscription content, log in via an institution to check access.
References
BellissimaF., ‘On the modal logic corresponding to diagonalizable algebra theory’, Boll. Un. Mat. Ital. (5), 15-B (1978), 915–930.
BernardiC., ‘The uniqueness of the fixed point in every diagonalizable algebra’ (The algebraization of the theories which express Theor, VIII), Studia Logica 35 (1976). 335–343.
Boolos, G., The Unprovability of Consistency. An Essay in Modal Logic, Cambridge U.P., 1979.
BoolosG., ‘Extremely undecidable sentences’, J. Symbolic Logic, 47 (1982) 191–196.
Gentzen G., Collected Papers, North Holland, 1969.
GödelK., ‘Eine Interpretation des intuitionistischen Aussagenkalküls‘, Ergebnisse eines Mathematischen Kolloquiums 4 (1933), 39–40.
Kleene, S. C., Mathematical Logic. Wiley, 1967.
LeivantD., ‘On the proof theory of the modal logic for arithmetic provability’, J. Symbolic Logic 46 (1981), 531–538.
LöbM. H., ‘Solution of a problem of Leon Henkin’, J. Symbolic 20 (1955), 115–118.
MirolliM., ‘On the axiomatization of finite frames of the modal system GL’, Boll. Un. Mat. Ital. (5) 17-B (1980), 1075–1085.
MontagnaF., ‘On the diagonalizable algebra of Peano arithmetic’, Boll. Un. Mat. Ital. (5) 16-B (1979), 795–812.
SambinG., ‘An effective fixed point theorem in intuitionistic diagonalizable algebras’ (The algebraization of the theories which express Theor, IX), Studia Logica 35 (1976), 345–361.
SambinG. and ValentiniS., ‘A modal sequent calculus for a fragment of arithmetic’, Studia Logica 39, (1980), 245–256.
Sambin, G. and Valentini, S., ‘Is there a syntactic proof of cut elimination for GL?’, submitted to J. Symbolic Logic.
Smorynski, C., ‘Beth's theorem and self-referential sentences, Logic Colloquium '77, A. Macintyre, L. Pacholski, J. Paris (eds), North Holland, 1978.
Smorynski, C., ‘Fixed point algebra’, to appear.
SmorynskiC., ‘Review to [3]’, J. Symbolic Logic 46 (1981), 871–873.
Solitro, U. and Valentini, S., ‘The modal logic of consistency assertion of Peano Arithmetic’, Z. Math. Logik Grundlag. Math., to appear.
SolovayR. M., ‘Provability interpretations of modal logic’, Israel J. Math. 25 (1976), 287–304.
Takeuti, G., Proof Theory, North Holland, 1975.
UrsiniA., ‘Intuitionistic diagonalizable algebras’, Alg. Universalis 9 (1979), 229–237.
ValentiniS., ‘Cut elimination in a modal sequent calculus for K’, Boll. Un. Mat. Ital. (6) 1-B (1982), 119–130
Valentini, S., ‘The modal logic of provability: cut elimination’, submitted to J. Philosophical Logic.
Visser, A., ‘Aspect of diagonalization and provability’, dissertation, University of Utrecht, 1981.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sambin, G., Valentini, S. The modal logic of provability. The sequential approach. J Philos Logic 11, 311–342 (1982). https://doi.org/10.1007/BF00293433
Issue Date:
DOI: https://doi.org/10.1007/BF00293433