David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Studia Logica 99 (1-3):249-267 (2011)
In a previous paper [ 21 ] all extensions of Johansson’s minimal logic J with the weak interpolation property WIP were described. It was proved that WIP is decidable over J. It turned out that the weak interpolation problem in extensions of J is reducible to the same problem over a logic Gl, which arises from J by adding tertium non datur. In this paper we consider extensions of the logic Gl. We prove that only finitely many logics over Gl have the Craig interpolation property CIP, the restricted interpolation property IPR or the projective Beth property PBP. The full list of Gl-logics with the mentioned properties is found, and their description is given. We note that IPR and PBP are equivalent over Gl. It is proved that CIP, IPR and PBP are decidable over the logic Gl
|Keywords||Minimal logic interpolation definability amalgamation|
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References found in this work BETA
William Craig (1957). Three Uses of the Herbrand-Gentzen Theorem in Relating Model Theory and Proof Theory. Journal of Symbolic Logic 22 (3):269-285.
Larisa Maksimova (2000). Intuitionistic Logic and Implicit Definability. Annals of Pure and Applied Logic 105 (1-3):83-102.
J. C. C. McKinsey & Alfred Tarski (1948). Some Theorems About the Sentential Calculi of Lewis and Heyting. Journal of Symbolic Logic 13 (1):1-15.
Sergei P. Odintsov (2004). Logic of Classical Refutability and Class of Extensions of Minimal Logic. Logic and Logical Philosophy 9:91.
Helena Rasiowa (1963). The Mathematics of Metamathematics. Warszawa, Państwowe Wydawn. Naukowe.
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