David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 59 (3):737-756 (1994)
This paper discusses lower bounds for proof length, especially as measured by number of steps (inferences). We give the first publicly known proof of Gödel's claim that there is superrecursive (in fact. unbounded) proof speedup of (i + 1)st-order arithmetic over ith-order arithmetic, where arithmetic is formalized in Hilbert-style calculi with + and · as function symbols or with the language of PRA. The same results are established for any weakly schematic formalization of higher-order logic: this allows all tautologies as axioms and allows all generalizations of axioms as axioms. Our first proof of Gödel's claim is based on self-referential sentences: we give a second proof that avoids the use of self-reference based loosely on a method of Statman
|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
Cezary Cieśliński (2010). Deflationary Truth and Pathologies. Journal of Philosophical Logic 39 (3):325 - 337.
Jeffrey Ketland (2005). Some More Curious Inferences. Analysis 65 (285):18–24.
Matthias Baaz & Piotr Wojtylak (2008). Generalizing Proofs in Monadic Languages. Annals of Pure and Applied Logic 154 (2):71-138.
Similar books and articles
Mateja Jamnik, Alan Bundy & Ian Green (1999). On Automating Diagrammatic Proofs of Arithmetic Arguments. Journal of Logic, Language and Information 8 (3):297-321.
Raymond M. Smullyan (1985). Uniform Self-Reference. Studia Logica 44 (4):439 - 445.
Jan Krajíček (1995). Bounded Arithmetic, Propositional Logic, and Complexity Theory. Cambridge University Press.
Jan Krajíček (1997). Interpolation Theorems, Lower Bounds for Proof Systems, and Independence Results for Bounded Arithmetic. Journal of Symbolic Logic 62 (2):457-486.
N. Shankar (1994). Metamathematics, Machines, and Gödel's Proof. Cambridge University Press.
Jeremy Avigad (1996). Formalizing Forcing Arguments in Subsystems of Second-Order Arithmetic. Annals of Pure and Applied Logic 82 (2):165-191.
Francesco Berto (2009). The Gödel Paradox and Wittgenstein's Reasons. Philosophia Mathematica 17 (2):208-219.
Pavel Hrubeš (2007). Lower Bounds for Modal Logics. Journal of Symbolic Logic 72 (3):941 - 958.
Maria Luisa Bonet & Samuel R. Buss (1993). The Deduction Rule and Linear and Near-Linear Proof Simulations. Journal of Symbolic Logic 58 (2):688-709.
Added to index2009-01-28
Total downloads9 ( #155,891 of 1,099,016 )
Recent downloads (6 months)1 ( #287,293 of 1,099,016 )
How can I increase my downloads?