Higher complexity search problems for bounded arithmetic and a formalized no-gap theorem

Archive for Mathematical Logic 50 (7):665-680 (2011)
  Copy   BIBTEX


We give a new characterization of the strict $$\forall {\Sigma^b_j}$$ sentences provable using $${\Sigma^b_k}$$ induction, for 1 ≤ j ≤ k. As a small application we show that, in a certain sense, Buss’s witnessing theorem for strict $${\Sigma^b_k}$$ formulas already holds over the relatively weak theory PV. We exhibit a combinatorial principle with the property that a lower bound for it in constant-depth Frege would imply that the narrow CNFs with short depth j Frege refutations form a strict hierarchy with j, and hence that the relativized bounded arithmetic hierarchy can be separated by a family of $$\forall {\Sigma^b_1}$$ sentences.



    Upload a copy of this work     Papers currently archived: 92,100

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Bounded arithmetic, propositional logic, and complexity theory.Jan Krajíček - 1995 - New York, NY, USA: Cambridge University Press.
On interpretations of bounded arithmetic and bounded set theory.Richard Pettigrew - 2009 - Notre Dame Journal of Formal Logic 50 (2):141-152.
On interpreting Chaitin's incompleteness theorem.Panu Raatikainen - 1998 - Journal of Philosophical Logic 27 (6):569-586.
Parallel strategies.Pavel Pudlák - 2003 - Journal of Symbolic Logic 68 (4):1242-1250.
Infinite substructure lattices of models of Peano Arithmetic.James H. Schmerl - 2010 - Journal of Symbolic Logic 75 (4):1366-1382.
Notes on polynomially bounded arithmetic.Domenico Zambella - 1996 - Journal of Symbolic Logic 61 (3):942-966.
Approximate Counting in Bounded Arithmetic.Emil Jeřábek - 2007 - Journal of Symbolic Logic 72 (3):959 - 993.


Added to PP

55 (#291,308)

6 months
5 (#644,465)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations