{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,5]],"date-time":"2023-10-05T06:11:35Z","timestamp":1696486295595},"reference-count":8,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2016,4,1]],"date-time":"2016-04-01T00:00:00Z","timestamp":1459468800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2016,5]]},"abstract":"<jats:p>In o\u2010minimal structures, every cell is definably connected and every definable set is a finite union of its definably connected components. In this note, we introduce pseudo definably connected definable sets in weakly o\u2010minimal structures having strong cell decomposition, and prove that every strong cell in those structures is pseudo definably connected. It follows that every definable set can be written as a finite union of its pseudo definably connected components. We also show that the projections of pseudo definably connected definable sets are pseudo definably connected. Finally, we compare pseudo definable connectedness with (recently introduced) weak definable connectedness of definable sets in weakly o\u2010minimal structures.<\/jats:p>","DOI":"10.1002\/malq.201400034","type":"journal-article","created":{"date-parts":[[2016,4,2]],"date-time":"2016-04-02T19:33:02Z","timestamp":1459625582000},"page":"241-248","source":"Crossref","is-referenced-by-count":0,"title":["Pseudo definably connected definable sets"],"prefix":"10.1002","volume":"62","author":[{"given":"Jafar S.","family":"Eivazloo","sequence":"first","affiliation":[{"name":"Department of Mathematics University of Tabriz 29 Bahman Bld, Tabriz 51666\u201014766 Islamic Republic of Iran"}]},{"given":"Somayyeh","family":"Tari","sequence":"additional","affiliation":[{"name":"Department of Mathematics University of Tabriz 29 Bahman Bld, Tabriz 51666\u201014766 Islamic Republic of Iran"},{"name":"Department of Mathematics Azarbaijan Shahid Madani University Kilometer 35, Tabriz\/Azarshahr Road, Tabriz 53714\u2010161 Islamic Republic of Iran"}]}],"member":"311","published-online":{"date-parts":[[2016,4]]},"reference":[{"key":"e_1_2_6_2_1","doi-asserted-by":"publisher","DOI":"10.2307\/2273866"},{"key":"e_1_2_6_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-014-0372-0"},{"key":"e_1_2_6_4_1","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1090\/S0002-9947-1986-0833698-1","article-title":"Definable sets in ordered structures II","volume":"295","author":"Knight J. F.","year":"1986","journal-title":"Trans. Amer. Math. Soc."},{"key":"e_1_2_6_5_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-00-02633-7"},{"key":"e_1_2_6_6_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1986-0833697-X"},{"key":"e_1_2_6_7_1","volume-title":"London Mathematical Society Lecture Notes Series Vol. 248","author":"Dries L.","year":"1998"},{"key":"e_1_2_6_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2008.01.009"},{"key":"e_1_2_6_9_1","doi-asserted-by":"publisher","DOI":"10.1002\/malq.201200016"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.201400034","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.201400034","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,4]],"date-time":"2023-10-04T22:57:31Z","timestamp":1696460251000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.201400034"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,4]]},"references-count":8,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2016,5]]}},"alternative-id":["10.1002\/malq.201400034"],"URL":"https:\/\/doi.org\/10.1002\/malq.201400034","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,4]]}}}