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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