{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,19]],"date-time":"2023-10-19T05:20:24Z","timestamp":1697692824875},"reference-count":9,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2007,9,26]],"date-time":"2007-09-26T00:00:00Z","timestamp":1190764800000},"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":[[2007,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Local sentences were introduced by Ressayre in [6] who proved certain remarkable stretching theorems establishing the equivalence between the existence of finite models for these sentences and the existence of some infinite well ordered models. Two of these stretching theorems were only proved under certain large cardinal axioms but the question of their exact (consistency) strength was left open in [4]. Here we solve this problem, using a combinatorial result of J. H. Schmerl [7]. In fact, we show that the stretching principles are equivalent to the existence of <jats:italic>n<\/jats:italic> \u2010Mahlo cardinals for appropriate integers <jats:italic>n<\/jats:italic>. This is done by proving first that for every integer <jats:italic>n<\/jats:italic>, there is a local sentence <jats:italic>\u03c6<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic> <\/jats:sub> having well ordered models of order type <jats:italic>\u03c4<\/jats:italic>, for every infinite ordinal <jats:italic>\u03c4<\/jats:italic> &gt; <jats:italic>\u03c9<\/jats:italic> which is not an <jats:italic>n<\/jats:italic> \u2010Mahlo cardinal. (\u00a9 2007 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200610049","type":"journal-article","created":{"date-parts":[[2007,9,26]],"date-time":"2007-09-26T12:46:39Z","timestamp":1190810799000},"page":"558-563","source":"Crossref","is-referenced-by-count":0,"title":["Local sentences and Mahlo cardinals"],"prefix":"10.1002","volume":"53","author":[{"given":"Olivier","family":"Finkel","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stevo","family":"Todorcevic","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2007,9,26]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(99)00286-8"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2004.03.025"},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","unstructured":"O.Finkel On decidability properties of local sentences. In: Proceedings of the 11th Workshop on Logic Language Information and Computation WoLLIC 2004. Electronic Notes in Theoretical Computer Science 123 pp. 75\u201392 (Elsevier 2005).","DOI":"10.1016\/j.entcs.2004.05.013"},{"key":"e_1_2_1_4_3","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2006.08.004"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.2307\/2275676"},{"key":"e_1_2_1_6_2","unstructured":"T.Jech Set Theory Third Edition (Springer 2002)."},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.2307\/2274601"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.2307\/1996779"},{"key":"e_1_2_1_9_2","unstructured":"H.Friedman Tranfer principles in set theory. Draft 1997. Available from:http:\/\/www.math.ohio\u2010state.edu\/\u223cfriedman\/manuscripts.html"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200610049","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.200610049","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T15:08:38Z","timestamp":1697641718000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.200610049"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,9,26]]},"references-count":9,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2007,11]]}},"alternative-id":["10.1002\/malq.200610049"],"URL":"https:\/\/doi.org\/10.1002\/malq.200610049","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,9,26]]}}}