New relations and separations of conjectures about incompleteness in the finite domain
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00561027" target="_blank" >RIV/67985840:_____/22:00561027 - isvavai.cz</a>
Výsledek na webu
<a href="https://doi.org/10.1017/jsl.2021.99" target="_blank" >https://doi.org/10.1017/jsl.2021.99</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/jsl.2021.99" target="_blank" >10.1017/jsl.2021.99</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
New relations and separations of conjectures about incompleteness in the finite domain
Popis výsledku v původním jazyce
In [20] Krajíček and Pudlák discovered connections between problems in computational complexity and the lengths of first-order proofs of finite consistency statements. Later Pudlák [25] studied more statements that connect provability with computational complexity and conjectured that they are true. All these conjectures are at least as strong as [23-25].One of the problems concerning these conjectures is to find out how tightly they are connected with statements about computational complexity classes. Results of this kind had been proved in [20, 22].In this paper, we generalize and strengthen these results. Another question that we address concerns the dependence between these conjectures. We construct two oracles that enable us to answer questions about relativized separations asked in [19, 25] (i.e., for the pairs of conjectures mentioned in the questions, we construct oracles such that one conjecture from the pair is true in the relativized world and the other is false and vice versa). We also show several new connections between the studied conjectures. In particular, we show that the relation between the finite reflection principle and proof systems for existentially quantified Boolean formulas is similar to the one for finite consistency statements and proof systems for non-quantified propositional tautologies.
Název v anglickém jazyce
New relations and separations of conjectures about incompleteness in the finite domain
Popis výsledku anglicky
In [20] Krajíček and Pudlák discovered connections between problems in computational complexity and the lengths of first-order proofs of finite consistency statements. Later Pudlák [25] studied more statements that connect provability with computational complexity and conjectured that they are true. All these conjectures are at least as strong as [23-25].One of the problems concerning these conjectures is to find out how tightly they are connected with statements about computational complexity classes. Results of this kind had been proved in [20, 22].In this paper, we generalize and strengthen these results. Another question that we address concerns the dependence between these conjectures. We construct two oracles that enable us to answer questions about relativized separations asked in [19, 25] (i.e., for the pairs of conjectures mentioned in the questions, we construct oracles such that one conjecture from the pair is true in the relativized world and the other is false and vice versa). We also show several new connections between the studied conjectures. In particular, we show that the relation between the finite reflection principle and proof systems for existentially quantified Boolean formulas is similar to the one for finite consistency statements and proof systems for non-quantified propositional tautologies.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10101 - Pure mathematics
Návaznosti výsledku
Projekt
—
Návaznosti
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Ostatní
Rok uplatnění
2022
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Journal of Symbolic Logic
ISSN
0022-4812
e-ISSN
1943-5886
Svazek periodika
87
Číslo periodika v rámci svazku
3
Stát vydavatele periodika
US - Spojené státy americké
Počet stran výsledku
26
Strana od-do
912-937
Kód UT WoS článku
000847361900005
EID výsledku v databázi Scopus
2-s2.0-85120650154