Abstract
This paper studies a propositional logic which is obtained by interpreting implication as formal provability. It is also the logic of finite irreflexive Kripke Models.
A Kripke Model completeness theorem is given and several completeness theorems for interpretations into Provability Logic and Peano Arithmetic.
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References
G. Boolos,The Unprovability of Consistency, Cambridge University Press, Cambridge 1979.
G. Boolos,Provability, truth and modal logic,Journal of Philosophical Logic 9 (1980), pp. 1–7.
M. A. Dummett,A propositional calculus with a denumerable matrix,The Journal of Symbolic Logic 24 (1959), pp. 97–106.
M. A. Dummett,Elements of Intuitionism, Clarendon Press, Oxford, 1977.
R. Goldblatt,Arithmetical necessity, provability and intuitionistic logic,Theoria 44 (1978), pp. 38–46.
C. Smoryński,Investigations of Intuitionistic Formal Systems by Means of Kripke Models, thesis.
C. Smoryński,Calculating self-referential statements I: explicit calculations,Studia Logica 38 (1979), pp. 17–36.
C. Smokyński,Calculating self-referential statements II: non-explicit calculations,Fundamenta Mathematicae, to appear.
R. M. Solovay,Provability interpretations of modal logic,Israel Journal of Mathematics 25 (1976), pp. 287–304.
A. S. Troelstra (ed.),Metamathematical Investigation of Intuitionistic Arithmetic and Analysis, Lecture Notes in Math. 344, Springer Verlag, Berlin, 1973.
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Visser, A. A propositional logic with explicit fixed points. Stud Logica 40, 155–175 (1981). https://doi.org/10.1007/BF01874706
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DOI: https://doi.org/10.1007/BF01874706