On gödel's theorems on lengths of proofs I: Number of lines and speedup for arithmetics

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)
DOI 10.2307/2275906
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 15,974
External links
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.

Add more references

Citations of this work BETA
Martin Fischer (2014). Truth and Speed-Up. Review of Symbolic Logic 7 (2):319-340.
Cezary Cieśliński (2010). Deflationary Truth and Pathologies. Journal of Philosophical Logic 39 (3):325 - 337.

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

14 ( #180,581 of 1,725,806 )

Recent downloads (6 months)

5 ( #134,315 of 1,725,806 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.