{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T09:34:46Z","timestamp":1772357686874,"version":"3.50.1"},"reference-count":13,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2016,6]]},"abstract":"<jats:p> We show that many principles of first-order arithmetic, previously only known to lie strictly between [Formula: see text]-induction and [Formula: see text]-induction, are equivalent to the well-foundedness of [Formula: see text]. Among these principles are the iteration of partial functions ([Formula: see text]) of H\u00e1jek and Paris, the bounded monotone enumerations principle (non-iterated, [Formula: see text]) by Chong, Slaman, and Yang, the relativized Paris\u2013Harrington principle for pairs, and the totality of the relativized Ackermann\u2013P\u00e9ter function. With this we show that the well-foundedness of [Formula: see text] is a far more widespread than usually suspected. Further, we investigate the [Formula: see text]-iterated version of the bounded monotone iterations principle ([Formula: see text]), and show that it is equivalent to the well-foundedness of the ([Formula: see text])-height [Formula: see text]-tower [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0219061316500045","type":"journal-article","created":{"date-parts":[[2016,6,10]],"date-time":"2016-06-10T00:25:40Z","timestamp":1465518340000},"page":"1650004","source":"Crossref","is-referenced-by-count":13,"title":["On principles between \u22111- and \u22112-induction, and monotone enumerations"],"prefix":"10.1142","volume":"16","author":[{"given":"Alexander P.","family":"Kreuzer","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, National University of Singapore, Block S17, 10 Lower Kent Ridge Road, Singapore 119076, Singapore"}]},{"given":"Keita","family":"Yokoyama","sequence":"additional","affiliation":[{"name":"School of Information Science, Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan"}]}],"member":"219","published-online":{"date-parts":[[2016,7,4]]},"reference":[{"key":"S0219061316500045BIB001","author":"Bovykin A.","year":"2005","journal-title":"Ann. Pure Appl. Logic"},{"key":"S0219061316500045BIB002","doi-asserted-by":"publisher","DOI":"10.2307\/2275219"},{"key":"S0219061316500045BIB003","doi-asserted-by":"publisher","DOI":"10.2307\/2694910"},{"key":"S0219061316500045BIB004","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-09-10115-6"},{"key":"S0219061316500045BIB005","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-2014-00789-X"},{"issue":"1","key":"S0219061316500045BIB007","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1007\/BF02017489","volume":"26","author":"H\u00e1jek P.","year":"1986","journal-title":"Arch. Math. Logik Grundlag"},{"key":"S0219061316500045BIB008","series-title":"Perspectives in Mathematical Logic","volume-title":"Metamathematics of First-Order Arithmetic","author":"H\u00e1jek P.","year":"1998"},{"key":"S0219061316500045BIB010","series-title":"Lecture Notes Series. Institute for Mathematical Sciences, National University of Singapore","volume-title":"Slicing the Truth: On the Computable and Reverse Mathematics of Combinatorial Principles","volume":"28","author":"Hirschfeldt D. R.","year":"2015"},{"key":"S0219061316500045BIB011","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1174668391"},{"key":"S0219061316500045BIB012","doi-asserted-by":"publisher","DOI":"10.2307\/2006985"},{"key":"S0219061316500045BIB013","doi-asserted-by":"publisher","DOI":"10.2307\/2274585"},{"key":"S0219061316500045BIB014","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511581007"},{"key":"S0219061316500045BIB015","doi-asserted-by":"publisher","DOI":"10.1002\/malq.201200047"}],"container-title":["Journal of Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219061316500045","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T22:59:34Z","timestamp":1565132374000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219061316500045"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,6]]},"references-count":13,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2016,7,4]]},"published-print":{"date-parts":[[2016,6]]}},"alternative-id":["10.1142\/S0219061316500045"],"URL":"https:\/\/doi.org\/10.1142\/s0219061316500045","relation":{},"ISSN":["0219-0613","1793-6691"],"issn-type":[{"value":"0219-0613","type":"print"},{"value":"1793-6691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,6]]}}}