David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 56 (2):385-424 (1991)
We present a survey of proof theory in the USSR beginning with the paper by Kolmogorov  and ending (mostly) in 1969; the last two sections deal with work done by A. A. Markov and N. A. Shanin in the early seventies, providing a kind of effective interpretation of negative arithmetic formulas. The material is arranged in chronological order and subdivided according to topics of investigation. The exposition is more detailed when the work is little known in the West or the original presentation can be improved using notions or results which appeared later. This includes such topics as Novikov's cut-elimination method (regular formulas) and Maslov's inverse method for the predicate logic
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Helmut Schwichtenberg & Christoph Senjak (2013). Minimal From Classical Proofs. Annals of Pure and Applied Logic 164 (6):740-748.
Similar books and articles
Robin Hirsch, Ian Hodkinson & Roger D. Maddux (2002). Relation Algebra Reducts of Cylindric Algebras and an Application to Proof Theory. Journal of Symbolic Logic 67 (1):197-213.
George Tourlakis (2010). On the Proof-Theory of Two Formalisations of Modal First-Order Logic. Studia Logica 96 (3):349-373.
Jan Krajíček (1997). Interpolation Theorems, Lower Bounds for Proof Systems, and Independence Results for Bounded Arithmetic. Journal of Symbolic Logic 62 (2):457-486.
Peter Aczel, Harold Simmons & S. S. Wainer (eds.) (1992). Proof Theory: A Selection of Papers From the Leeds Proof Theory Programme, 1990. Cambridge University Press.
Jan Krajíček (1995). Bounded Arithmetic, Propositional Logic, and Complexity Theory. Cambridge University Press.
H. Kushida & M. Okada (2003). A Proof-Theoretic Study of the Correspondence of Classical Logic and Modal Logic. Journal of Symbolic Logic 68 (4):1403-1414.
Gregory Landini (1996). The Definability of the Set of Natural Numbers in the 1925 Principia Mathematica. Journal of Philosophical Logic 25 (6):597 - 615.
A. S. Troelstra (2000). Basic Proof Theory. Cambridge University Press.
G. Mints (1999). Cut-Elimination for Simple Type Theory with an Axiom of Choice. Journal of Symbolic Logic 64 (2):479-485.
Added to index2009-01-28
Total downloads24 ( #71,831 of 1,101,088 )
Recent downloads (6 months)2 ( #177,551 of 1,101,088 )
How can I increase my downloads?