Arithmetical and Hyperarithmetical Worm Battles

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Arithmetical and Hyperarithmetical Worm Battles
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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