{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T12:38:41Z","timestamp":1740141521452,"version":"3.37.3"},"reference-count":23,"publisher":"Oxford University Press (OUP)","issue":"8","license":[{"start":{"date-parts":[[2022,10,27]],"date-time":"2022-10-27T00:00:00Z","timestamp":1666828800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"name":"FWO-FWF Lead Agency","award":["G030620N"],"award-info":[{"award-number":["G030620N"]}]},{"DOI":"10.13039\/501100004837","name":"Spanish Ministry of Science and Innovation","doi-asserted-by":"publisher","award":["PID2019-107667GB-I00"],"award-info":[{"award-number":["PID2019-107667GB-I00"]}],"id":[{"id":"10.13039\/501100004837","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,12,9]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Japaridze\u2019s provability logic ${\\operatorname {GLP}}$ has one modality $[n]$ for each natural number and has been used by Beklemishev for a proof theoretic analysis of Peano arithmetic (${\\operatorname {PA}}$) and related theories. Among other benefits, this analysis yields the so-called Every Worm Dies (${\\operatorname {EWD}}$) principle, a natural combinatorial statement independent of ${\\operatorname {PA}}$. Recently, Beklemishev and Pakhomov have studied notions of provability corresponding to transfinite modalities in ${\\operatorname {GLP}}$. We show that indeed the natural transfinite extension of ${\\operatorname {GLP}}$ is sound for this interpretation and yields independent combinatorial principles for the second-order theory ${\\operatorname {ACA}}$ of arithmetical comprehension with full induction. We also provide restricted versions of ${\\operatorname {EWD}}$ related to the fragments ${\\operatorname {I\\varSigma }}_n$ of PA. In order to prove the latter, we show that standard Hardy functions majorize their variants based on tree ordinals.<\/jats:p>","DOI":"10.1093\/logcom\/exac067","type":"journal-article","created":{"date-parts":[[2022,10,27]],"date-time":"2022-10-27T10:51:13Z","timestamp":1666867873000},"page":"1558-1584","source":"Crossref","is-referenced-by-count":0,"title":["Arithmetical and Hyperarithmetical Worm Battles"],"prefix":"10.1093","volume":"32","author":[{"given":"David","family":"Fern\u00c1ndez-Duque","sequence":"first","affiliation":[{"name":"Department of Mathematics WE16 , Ghent University, 9000 Ghent, Belgium, Institute of Computer Science, Czech Academy of Sciences, 182 07 Prague, Czech Republic"}]},{"given":"Joost J","family":"Joosten","sequence":"additional","affiliation":[{"name":"Department of Philosophy , University of Barcelona, Catalonia, 08001 Barcelona, Spain"}]},{"given":"Fedor","family":"Pakhomov","sequence":"additional","affiliation":[{"name":"Department of Mathematics WE16 , Ghent University, 9000 Ghent, Belgium"}]},{"given":"Konstantinos","family":"Papafilippou","sequence":"additional","affiliation":[{"name":"Department of Mathematics WE16 , Ghent University, 9000 Ghent, Belgium"}]},{"given":"Andreas","family":"Weiermann","sequence":"additional","affiliation":[{"name":"Department of Mathematics WE16 , Ghent University, 9000 Ghent, Belgium"}]}],"member":"286","published-online":{"date-parts":[[2022,10,27]]},"reference":[{"key":"2023072715335719100_ref1","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/S0168-0072(96)00045-0","article-title":"Induction rules, reflection principles, and provably recursive functions","volume":"85","author":"Beklemishev","year":"1997","journal-title":"Annals of Pure and Applied Logic"},{"key":"2023072715335719100_ref2","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1007\/s00153-002-0158-7","article-title":"Proof-theoretic analysis by iterated 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