{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,4]],"date-time":"2023-10-04T06:40:40Z","timestamp":1696401640536},"reference-count":14,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2014,5,11]],"date-time":"2014-05-11T00:00:00Z","timestamp":1399766400000},"content-version":"vor","delay-in-days":10,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2014,5]]},"abstract":"We show how one can obtain solutions to the Arzel\u00e0\u2010Ascoli theorem using suitable applications of the Bolzano\u2010Weierstra\u00df principle. With this, we can apply the results from and obtain a classification of the strength of instances of the Arzel\u00e0\u2010Ascoli theorem and a variant of it. Let be the statement that each equicontinuous sequence of functions contains a subsequence that converges uniformly with the rate and let be the statement that each such sequence contains a subsequence which converges uniformly but possibly without any rate. We show that is instance\u2010wise equivalent, over , to the Bolzano\u2010Weierstra\u00df principle and that is instance\u2010wise equivalent, over , to , and thus to the strong cohesive principle (). Moreover, we show that over the principles , and are equivalent.<\/jats:p>","DOI":"10.1002\/malq.201200076","type":"journal-article","created":{"date-parts":[[2014,5,11]],"date-time":"2014-05-11T18:20:01Z","timestamp":1399832401000},"page":"177-183","source":"Crossref","is-referenced-by-count":0,"title":["From Bolzano\u2010Weierstra\u00df to Arzel\u00e0\u2010Ascoli"],"prefix":"10.1002","volume":"60","author":[{"given":"Alexander P.","family":"Kreuzer","sequence":"first","affiliation":[{"name":"Laboratoire de l'Informatique du Parall\u00e9lisme (LIP) \u00c9cole Normale Sup\u00e9rieure de Lyon 46\u00a0All\u00e9e d'Italie, 69364 Lyon Cedex 07 France"},{"name":"Department of Mathematics Faculty of Science National University of Singapore Block S17, 10 Lower Kent Ridge Road, Singapore 119076 Singapore"}]}],"member":"311","published-online":{"date-parts":[[2014,5,11]]},"reference":[{"key":"e_1_2_6_2_1","doi-asserted-by":"publisher","DOI":"10.2178\/bsl\/1294186663"},{"key":"e_1_2_6_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2011.10.006"},{"key":"e_1_2_6_4_1","doi-asserted-by":"publisher","DOI":"10.2307\/2694910"},{"key":"e_1_2_6_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2012.02.025"},{"key":"e_1_2_6_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2008.09.018"},{"key":"e_1_2_6_7_1","first-page":"81","volume-title":"Studies in Logic and the Foundations of Mathematics","author":"Kleene S. C.","year":"1959"},{"key":"e_1_2_6_8_1","first-page":"115","volume-title":"Lecture Notes in Logic","author":"Kohlenbach U.","year":"1998"},{"key":"e_1_2_6_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(99)00036-6"},{"key":"e_1_2_6_10_1","volume-title":"Constructivity in Mathematics: Proceedings of the Colloquium Held at Amsterdam, 1957","author":"Kreisel G.","year":"1959"},{"key":"e_1_2_6_11_1","doi-asserted-by":"publisher","DOI":"10.1002\/malq.201010008"},{"key":"e_1_2_6_12_1","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1344862165"},{"key":"e_1_2_6_13_1","doi-asserted-by":"publisher","DOI":"10.2307\/2274131"},{"key":"e_1_2_6_14_1","volume-title":"Perspectives in Logic","author":"Simpson S. G.","year":"2009"},{"key":"e_1_2_6_15_1","first-page":"255","volume-title":"Proceedings of the Third International Conference on Computability and Complexity in Analysis (CCA 2006)","author":"Ziegler M.","year":"2007"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.201200076","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.201200076","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,4]],"date-time":"2023-10-04T00:46:53Z","timestamp":1696380413000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.201200076"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,5]]},"references-count":14,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2014,5]]}},"alternative-id":["10.1002\/malq.201200076"],"URL":"https:\/\/doi.org\/10.1002\/malq.201200076","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,5]]}}}