Incompleteness in the finite domain

0487354 - MÚ 2019 RIV US eng J - Journal Article
Pudlák, Pavel
Incompleteness in the finite domain.
Bulletin of Symbolic Logic. Roč. 23, č. 4 (2017), s. 405-441. ISSN 1079-8986. E-ISSN 1943-5894
EU Projects: European Commission(XE) 339691 - FEALORA
Institutional support: RVO:67985840
Keywords : finite domain
OECD category: Pure mathematics
Impact factor: 0.613, year: 2017
https://www.cambridge.org/core/journals/bulletin-of-symbolic-logic/article/incompleteness-in-the-finite-domain/D239B1761A73DCA534A4805A76D81C76

Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond NP coNP. These conjectures formally connect computational complexity with the difficulty of proving some sentences, which means that high computational complexity of a problem associated with a sentence implies that the sentence is not provable in a weak theory, or requires a long proof. Another reason for putting forward these conjectures is that some results in proof complexity seem to be special cases of such general statements and we want to formalize and fully understand these statements. Roughly speaking, we are trying to connect syntactic complexity, by which we mean the complexity of sentences and strengths of the theories in which they are provable, with the semantic concept of complexity of the computational problems represented by these sentences.
Permanent Link: http://hdl.handle.net/11104/0282020