{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,6,15]],"date-time":"2022-06-15T04:23:10Z","timestamp":1655266990870},"reference-count":10,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":6310,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1996,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The inverse of the distance between two structures<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200016820_inline1\" \/>\u2262<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200016820_inline2\" \/>of finite type<jats:italic>\u03c4<\/jats:italic>is naturally measured by the smallest integer<jats:italic>q<\/jats:italic>such that a sentence of quantifier rank<jats:italic>q<\/jats:italic>\u2212 1 is satisfied by<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200016820_inline1\" \/>but not by<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200016820_inline2\" \/>. In this way the space Str<jats:sup><jats:italic>\u03c4<\/jats:italic><\/jats:sup>of structures of type<jats:italic>\u03c4<\/jats:italic>is equipped with a pseudometric. The induced topology coincides with the elementary topology of Str<jats:sup><jats:italic>\u03c4<\/jats:italic><\/jats:sup>. Using the rudiments of the theory of uniform spaces, in this elementary note we prove the convergence of every Cauchy net of structures, for any type<jats:italic>\u03c4<\/jats:italic>.<\/jats:p>","DOI":"10.2307\/2275809","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:59:54Z","timestamp":1146956394000},"page":"1153-1157","source":"Crossref","is-referenced-by-count":1,"title":["Cauchy completeness in elementary logic"],"prefix":"10.1017","volume":"61","author":[{"given":"J. C.","family":"Cifuentes","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A. M.","family":"Sette","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"D.","family":"Mundici","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200016820_ref008","doi-asserted-by":"publisher","DOI":"10.2307\/1970235"},{"key":"S0022481200016820_ref004","volume-title":"Course de logique math\u00e9matique, tome 1","author":"Fra\u00efss\u00e9","year":"1967"},{"key":"S0022481200016820_ref006","volume-title":"The theory of models","author":"Karp","year":"1965"},{"key":"S0022481200016820_ref009","first-page":"785","volume":"51","author":"Mundici","year":"1986","journal-title":"Inverse topological systems and compactness in abstract model theory"},{"key":"S0022481200016820_ref005","doi-asserted-by":"publisher","DOI":"10.4064\/fm-51-3-195-228"},{"key":"S0022481200016820_ref007","volume-title":"General topology","author":"Kelley","year":"1955"},{"key":"S0022481200016820_ref003","doi-asserted-by":"crossref","DOI":"10.1515\/9781400882052","volume-title":"Continuous model theory","author":"Chang","year":"1966"},{"key":"S0022481200016820_ref001","volume-title":"Models and ultraproducts: An introduction","author":"Bell","year":"1969"},{"key":"S0022481200016820_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(93)90229-7"},{"key":"S0022481200016820_ref010","first-page":"705","volume-title":"Proceedings of the International Congress of Mathematics 1950","author":"Tarski","year":"1952"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200016820","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,14]],"date-time":"2020-04-14T14:23:02Z","timestamp":1586874182000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200016820\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,12]]},"references-count":10,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1996,12]]}},"alternative-id":["S0022481200016820"],"URL":"https:\/\/doi.org\/10.2307\/2275809","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,12]]}}}