{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,5]],"date-time":"2023-10-05T06:11:37Z","timestamp":1696486297311},"reference-count":11,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2016,5,27]],"date-time":"2016-05-27T00:00:00Z","timestamp":1464307200000},"content-version":"vor","delay-in-days":26,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"name":"Russian Foundation for Basic Research","award":["14-01-93105","16-01-00615"],"award-info":[{"award-number":["14-01-93105","16-01-00615"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2016,5]]},"abstract":"In set theory without the Axiom of Choice , we study the deductive strength of the statements (\u201cEvery partially ordered set without a maximal element has two disjoint cofinal subsets\u201d), (\u201cEvery partially ordered set without a maximal element has a countably infinite disjoint family of cofinal subsets\u201d), (\u201cEvery linearly ordered set without a maximum element has two disjoint cofinal subsets\u201d), and (\u201cEvery linearly ordered set without a maximum element has a countably infinite disjoint family of cofinal subsets\u201d).\nAmong various results, we prove that none of the above statements is provable without using some form of choice, is equivalent to , + (Dependent Choices) implies , does not imply in (Zermelo\u2010Fraenkel set theory with the Axiom of Extensionality modified in order to allow the existence of atoms), does not imply in (Zermelo\u2010Fraenkel set theory minus ) and (hence, ) is strictly weaker than in .<\/jats:p>","DOI":"10.1002\/malq.201400089","type":"journal-article","created":{"date-parts":[[2016,5,27]],"date-time":"2016-05-27T21:03:13Z","timestamp":1464382993000},"page":"155-176","source":"Crossref","is-referenced-by-count":5,"title":["On the set\u2010theoretic strength of the existence of disjoint cofinal sets in posets without maximal elements"],"prefix":"10.1002","volume":"62","author":[{"given":"Paul","family":"Howard","sequence":"first","affiliation":[{"name":"Department of Mathematics Eastern Michigan University Ypsilanti MI 48197 United States of America"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Denis I.","family":"Saveliev","sequence":"additional","affiliation":[{"name":"Institute for Information Transmission Problems Russian Academy of Sciences B. Karetny 19 127994 Moscow Russian Federation"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eleftherios","family":"Tachtsis","sequence":"additional","affiliation":[{"name":"Department of Mathematics University of the Aegean Karlovassi 83200 Samos Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2016,5,27]]},"reference":[{"key":"e_1_2_7_2_1","doi-asserted-by":"publisher","DOI":"10.2307\/2273477"},{"issue":"4","key":"e_1_2_7_3_1","first-page":"329","article-title":"A model without ultrafilters","volume":"25","author":"Blass A.","year":"1977","journal-title":"Bull. Acad. Polon. S\u00e9r. Sci. Math. Astr. Phys."},{"key":"e_1_2_7_4_1","doi-asserted-by":"publisher","DOI":"10.4064\/fm-97-2-111-122"},{"key":"e_1_2_7_5_1","volume-title":"Mathematical Surveys and Monographs Vol. 59","author":"Howard P.","year":"1998"},{"key":"e_1_2_7_6_1","volume-title":"Studies in Logic and the Foundations of Mathematics Vol. 75","author":"Jech T.","year":"1973"},{"key":"e_1_2_7_7_1","doi-asserted-by":"publisher","DOI":"10.4064\/fm-50-5-475-483"},{"key":"e_1_2_7_8_1","volume-title":"Studies in Logic and the Foundations of Mathematics Vol. 87","author":"Pincus D.","year":"1977"},{"key":"e_1_2_7_9_1","doi-asserted-by":"publisher","DOI":"10.2307\/2272420"},{"key":"e_1_2_7_10_1","unstructured":"D. I.Saveliev Cofinal subsets of ordered sets without the axiom of choice preprint."},{"key":"e_1_2_7_11_1","doi-asserted-by":"publisher","DOI":"10.4064\/ba63-1-1"},{"key":"e_1_2_7_12_1","doi-asserted-by":"publisher","DOI":"10.4064\/fm-6-1-45-95"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.201400089","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.201400089","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,4]],"date-time":"2023-10-04T22:57:41Z","timestamp":1696460261000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.201400089"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,5]]},"references-count":11,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2016,5]]}},"alternative-id":["10.1002\/malq.201400089"],"URL":"https:\/\/doi.org\/10.1002\/malq.201400089","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,5]]}}}