{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,30]],"date-time":"2023-09-30T10:40:12Z","timestamp":1696070412001},"reference-count":10,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2010,11,17]],"date-time":"2010-11-17T00:00:00Z","timestamp":1289952000000},"content-version":"vor","delay-in-days":4338,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1999,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We construct a recursive ultrapower <jats:italic>F\/U<\/jats:italic> such that <jats:italic>F\/U<\/jats:italic> is a tame 1\u2010model in the sense of [6, \u00a73] and <jats:italic>FU<\/jats:italic> is existentially incomplete in the models of II<jats:sub>2<\/jats:sub> arithmetic. This enables us to answer in the negative a question about closure with respect to recursive fibers of certain special semirings \u0393 of isols termed tame models by Barback. Erik Ellentuck had conjuctured that all such semirings enjoy the closure property in question. Our result is that while many do, some do not.<\/jats:p>","DOI":"10.1002\/malq.19990450204","type":"journal-article","created":{"date-parts":[[2010,11,17]],"date-time":"2010-11-17T16:30:55Z","timestamp":1290011455000},"page":"189-202","source":"Crossref","is-referenced-by-count":0,"title":["Existentially Incomplete Tame Models and a Conjecture of Ellentuck"],"prefix":"10.1002","volume":"45","author":[{"given":"Thomas G.","family":"McLaughlin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2010,11,17]]},"reference":[{"key":"e_1_2_1_2_2","first-page":"163","article-title":"Tame models in the isols","volume":"12","author":"Barback J.","year":"1986","journal-title":"Houston J. Math."},{"key":"e_1_2_1_3_2","doi-asserted-by":"crossref","first-page":"935","DOI":"10.1090\/S0002-9939-1993-1155592-0","article-title":"On the minimality of tame models in the isols","volume":"119","author":"Barback J.","year":"1993","journal-title":"Proc. Amer. Math. Soc."},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.2307\/2275256"},{"key":"e_1_2_1_5_2","series-title":"Lecture Notes in Mathematics 454","volume-title":"Forcing, Arithmetic, Division Rings","author":"Hirschfeld J.","year":"1982"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.2307\/2046244"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(90)90064-9"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01794985"},{"key":"e_1_2_1_9_2","doi-asserted-by":"crossref","first-page":"1141","DOI":"10.1090\/S0002-9939-1993-1116268-9","article-title":"Recursive fibers of RST isols","volume":"117","author":"McLaughlin T.","year":"1993","journal-title":"Proc. Amer. Math. Soc."},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19950410102"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.2307\/1970455"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19990450204","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19990450204","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19990450204","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,29]],"date-time":"2023-09-29T19:17:57Z","timestamp":1696015077000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19990450204"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,1]]},"references-count":10,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1999,1]]}},"alternative-id":["10.1002\/malq.19990450204"],"URL":"https:\/\/doi.org\/10.1002\/malq.19990450204","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,1]]}}}