{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,2]],"date-time":"2024-08-02T15:52:58Z","timestamp":1722613978679},"reference-count":4,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":5064,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1993,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>By suitably adapting an argument of Hirschfeld (see [2, Chapter 9]), we show that there is a single \u0394<jats:sub>1<\/jats:sub> formula that defeats \u201cbounded collection\u201d for any model of II<jats:sub>2<\/jats:sub> Arithmetic that is either a recursive ultrapower or an existentially complete model. Some related facts are noted. MSC: 03F30, 03C62.<\/jats:p>","DOI":"10.1002\/malq.19930390146","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T17:19:11Z","timestamp":1180199951000},"page":"431-435","source":"Crossref","is-referenced-by-count":3,"title":["A note on effective ultrapowers: Uniform failure of bounded collection"],"prefix":"10.1002","volume":"39","author":[{"given":"Thomas","family":"McLaughlin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02757881"},{"key":"e_1_2_1_3_2","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0064082","volume-title":"Forcing, Arithmetic, Division Rings. Lecture Notes in Mathematics 454","author":"Hirschfeld J.","year":"1975"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(90)90064-9"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0095652"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19930390146","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19930390146","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T21:00:02Z","timestamp":1698267602000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19930390146"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,1]]},"references-count":4,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1993,1]]}},"alternative-id":["10.1002\/malq.19930390146"],"URL":"https:\/\/doi.org\/10.1002\/malq.19930390146","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,1]]}}}