{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,1]],"date-time":"2025-12-01T02:52:03Z","timestamp":1764557523212},"reference-count":9,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2020,12]]},"abstract":"<jats:p> We propose a new method for constructing Turing ideals satisfying principles of reverse mathematics below the Chain\u2013Antichain ([Formula: see text]) Principle. Using this method, we are able to prove several new separations in the presence of Weak K\u00f6nig\u2019s Lemma ([Formula: see text]), including showing that [Formula: see text] does not imply the thin set theorem for pairs, and that the principle \u201cthe product of well-quasi-orders is a well-quasi-order\u201d is strictly between [Formula: see text] and the Ascending\/Descending Sequences principle, even in the presence of [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0219061320500178","type":"journal-article","created":{"date-parts":[[2020,1,31]],"date-time":"2020-01-31T08:32:19Z","timestamp":1580459539000},"page":"2050017","source":"Crossref","is-referenced-by-count":2,"title":["Constructing sequences one step at a time"],"prefix":"10.1142","volume":"20","author":[{"given":"Henry","family":"Towsner","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA 19104-6395, USA"}]}],"member":"219","published-online":{"date-parts":[[2020,3,25]]},"reference":[{"key":"S0219061320500178BIB001","series-title":"Lecture Notes in Logic","first-page":"104","volume-title":"Reverse Mathematics 2001","volume":"21","author":"Cholak P. A.","year":"2005"},{"issue":"3","key":"S0219061320500178BIB002","doi-asserted-by":"crossref","first-page":"683","DOI":"10.2178\/jsl\/1096901762","volume":"69","author":"Cholak P.","year":"2004","journal-title":"J. Symbolic Logic"},{"key":"S0219061320500178BIB005","unstructured":"D. R. Hirschfeldt,  Slicing the Truth, On the Computable and Reverse Mathematics of Combinatorial Principles, eds.   C. Chong,  Q. Feng,  T. A. Slaman,  W. Hugh Woodin and  Y. Yang,  Lecture Notes Series,  Institute for Mathematical Sciences, National University of Singapore, Vol.  28  (World Scientific Publishing Co. Pte. Ltd.,  Hackensack, NJ,  2015),  pp. xvi+214,  ISBN: 978-981-4612-61-6."},{"issue":"1","key":"S0219061320500178BIB006","doi-asserted-by":"crossref","first-page":"171","DOI":"10.2178\/jsl\/1174668391","volume":"72","author":"Hirschfeldt D. R.","year":"2007","journal-title":"J. Symbolic Logic"},{"issue":"2","key":"S0219061320500178BIB007","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1142\/S0219061313500074","volume":"13","author":"Lerman M.","year":"2013","journal-title":"J. Math. Log."},{"key":"S0219061320500178BIB008","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1007\/978-3-319-08019-2_33","volume-title":"Language, Life, Limits","volume":"8493","author":"Murakami S.","year":"2014"},{"key":"S0219061320500178BIB009","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1007\/978-3-319-40189-8_36","volume-title":"Pursuit of the Universal","volume":"9709","author":"Patey L.","year":"2016"},{"key":"S0219061320500178BIB011","unstructured":"S. G. Simpson,  Subsystems of Second Order Arithmetic,  2nd edn.  Perspectives in Logic  (Cambridge University Press,  Cambridge,  2009),  pp. xvi+444,  ISBN: 978-0-521-88439-6."},{"key":"S0219061320500178BIB012","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.aim.2014.05.003","volume":"261","author":"Wang W.","year":"2014","journal-title":"Adv. Math."}],"container-title":["Journal of Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219061320500178","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,20]],"date-time":"2020-11-20T10:25:36Z","timestamp":1605867936000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219061320500178"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,25]]},"references-count":9,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2020,12]]}},"alternative-id":["10.1142\/S0219061320500178"],"URL":"https:\/\/doi.org\/10.1142\/s0219061320500178","relation":{},"ISSN":["0219-0613","1793-6691"],"issn-type":[{"value":"0219-0613","type":"print"},{"value":"1793-6691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,3,25]]}}}