Arithmetical and Hyperarithmetical Worm Battles

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F22%3A00565843" target="_blank" >RIV/67985807:_____/22:00565843 - isvavai.cz</a>

Výsledek na webu

<a href="https://dx.doi.org/10.1093/logcom/exac067" target="_blank" >https://dx.doi.org/10.1093/logcom/exac067</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1093/logcom/exac067" target="_blank" >10.1093/logcom/exac067</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Arithmetical and Hyperarithmetical Worm Battles

Popis výsledku v původním jazyce

Japaridze's provability logic GLP has one modality [n] for each natural number and has been used by Beklemishev for a proof theoretic analysis of Peano arithmetic (PA) and related theories. Among other benefits, this analysis yields the so called Every Worm Dies (EWD) principle, a natural combinatorial statement independent of PA. Recently, Beklemishev and Pakhomov have studied notions of provability corresponding to transfinite modalities in GLP. We show that indeed the natural transfinite extension of GLP is sound for this interpretation and yields independent combinatorial principles for the second-order theory ACA of arithmetical comprehension with full induction. We also provide restricted versions of EWD related to the fragments I Sigma(n) of PA. In order to prove the latter, we show that standard Hardy functions majorize their variants based on tree ordinals.

Název v anglickém jazyce

Arithmetical and Hyperarithmetical Worm Battles

Popis výsledku anglicky

Japaridze's provability logic GLP has one modality [n] for each natural number and has been used by Beklemishev for a proof theoretic analysis of Peano arithmetic (PA) and related theories. Among other benefits, this analysis yields the so called Every Worm Dies (EWD) principle, a natural combinatorial statement independent of PA. Recently, Beklemishev and Pakhomov have studied notions of provability corresponding to transfinite modalities in GLP. We show that indeed the natural transfinite extension of GLP is sound for this interpretation and yields independent combinatorial principles for the second-order theory ACA of arithmetical comprehension with full induction. We also provide restricted versions of EWD related to the fragments I Sigma(n) of PA. In order to prove the latter, we show that standard Hardy functions majorize their variants based on tree ordinals.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Logic and Computation

ISSN

0955-792X

e-ISSN

1465-363X

Svazek periodika

32

Číslo periodika v rámci svazku

8

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

27

Strana od-do

1558-1584

Kód UT WoS článku

000873825500001

EID výsledku v databázi Scopus

—