Bimodal logics for extensions of arithmetical theories

Journal of Symbolic Logic 61 (1):91-124 (1996)
We characterize the bimodal provability logics for certain natural (classes of) pairs of recursively enumerable theories, mostly related to fragments of arithmetic. For example, we shall give axiomatizations, decision procedures, and introduce natural Kripke semantics for the provability logics of (IΔ 0 + EXP, PRA); (PRA, IΣ 1 ); (IΣ m , IΣ n ) for $1 \leq m etc. For the case of finitely axiomatized extensions of theories these results are extended to modal logics with propositional constants
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2307/2275600
 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: 30,876
Through your library
References found in this work BETA
On the Scheme of Induction for Bounded Arithmetic Formulas.A. J. Wilkie & J. B. Paris - 1987 - Annals of Pure and Applied Logic 35 (3):261-302.
Fragments of Arithmetic.Wilfried Sieg - 1983 - Annals of Pure and Applied Logic 28 (1):33-71.
Reflection Principles and Their Use for Establishing the Complexity of Axiomatic Systems.Georg Kreisel & Azriel Lévy - 1968 - Zeitschrift für Mathematische Logic Und Grundlagen der Mathematik 14 (1):97--142.
Reflection Principles and Their Use for Establishing the Complexity of Axiomatic Systems.G. Kreisel & A. Lévy - 1968 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 14 (7-12):97-142.

View all 14 references / Add more references

Citations of this work BETA
Iterated Local Reflection Versus Iterated Consistency.Lev Beklemishev - 1995 - Annals of Pure and Applied Logic 75 (1-2):25-48.

Add more citations

Similar books and articles
Added to PP index

Total downloads
10 ( #475,154 of 2,213,798 )

Recent downloads (6 months)
1 ( #411,016 of 2,213,798 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature