Interpolation and Definability over the Logic Gl

Studia Logica 99 (1-3):249-267 (2011)
Abstract
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
Categories (categorize this paper)
DOI 10.1007/s11225-011-9351-1
Options
 Save to my reading list
Follow the author(s)
Edit this record
My bibliography
Export citation
Find it on Scholar
Mark as duplicate
Request removal from index
Revision history
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 30,719
Through your library
References found in this work BETA
The Mathematics of Metamathematics.Helena Rasiowa - 1963 - Warszawa, Państwowe Wydawn. Naukowe.
Semantical Investigations in Heyting's Intuitionistic Logic.Dov M. Gabbay - 1986 - Journal of Symbolic Logic 51 (3):824-824.

View all 17 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles
Added to PP index
2011-09-22

Total downloads
7 ( #538,601 of 2,197,307 )

Recent downloads (6 months)
1 ( #299,047 of 2,197,307 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature