{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T00:12:54Z","timestamp":1782259974941,"version":"3.54.5"},"reference-count":9,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2004,10,1]],"date-time":"2004-10-01T00:00:00Z","timestamp":1096588800000},"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":[[2004,10]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper concerns intermediate structure lattices Lt(\ud835\udca9\/\u2133\ufe01), where \ud835\udca9 is an almost minimal elementary end extension of the model \u2133\ufe01 of Peano Arithmetic. For the purposes of this abstract only, let us say that \u2133\ufe01 attains <jats:italic>L<\/jats:italic> if <jats:italic>L<\/jats:italic> \u2245 Lt(\ud835\udca9\/\u2133\ufe01) for some almost minimal elementary end extension of \ud835\udca9. If <jats:italic>T<\/jats:italic> is a completion of PA and <jats:italic>L<\/jats:italic> is a finite lattice, then:<\/jats:p><jats:p>(A) If some model of <jats:italic>T<\/jats:italic> attains <jats:italic>L<\/jats:italic>, then every countable model of <jats:italic>T<\/jats:italic> does.<\/jats:p><jats:p>(B) If some rather classless, \u2135<jats:sub>1<\/jats:sub>\u2010saturated model of <jats:italic>T<\/jats:italic> attains <jats:italic>L<\/jats:italic>, then every model of <jats:italic>T<\/jats:italic> does. (\u00a9 2004 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200310118","type":"journal-article","created":{"date-parts":[[2004,10,4]],"date-time":"2004-10-04T16:01:01Z","timestamp":1096905661000},"page":"533-539","source":"Crossref","is-referenced-by-count":4,"title":["Substructure lattices and almost minimal end extensions of models of Peano arithmetic"],"prefix":"10.1002","volume":"50","author":[{"given":"James H.","family":"Schmerl","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2004,10]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.2307\/2272552"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.2307\/2272355"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(76)90002-4"},{"key":"e_1_2_1_5_2","doi-asserted-by":"crossref","unstructured":"J. H.Schmerl Substructure lattices of models of Peano Arithmetic. In: Logic Colloquium '84 pp. 225\u2013243 (North\u2010Holland Publ. Comp. Amsterdam 1986).","DOI":"10.1016\/S0049-237X(08)70465-8"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.2307\/2159151"},{"key":"e_1_2_1_7_2","doi-asserted-by":"crossref","unstructured":"J. H.Schmerl Rather classless highly saturated models of Peano Arithmetic. In: Logic Colloquium '96 (J. M. Larrazabal et al. eds.) Lecture Notes in Logic12 pp. 237\u2013246 (Springer\u2010Verlag Berlin et al. 1998).","DOI":"10.1007\/978-3-662-22110-5_10"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1190150284"},{"key":"e_1_2_1_9_2","doi-asserted-by":"crossref","unstructured":"J. H.Schmerl Diversity in substructures. In: Nonstandard Models of Arithmetic and Set Theory (A. Enayat and R. Kossak eds.) Contemporary Mathematics (Amer. Math. Soc. Providence 2004).","DOI":"10.1090\/conm\/361\/06593"},{"key":"e_1_2_1_10_2","unstructured":"S. F.Soprunov Lattices of nonstandard arithmetics (in Russian). Studies in nonclassical logics and set theory pp. 203\u2013223 (\u201cNauka\u201d Moscow 1979)."}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200310118","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.200310118","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T21:00:38Z","timestamp":1697662838000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.200310118"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,10]]},"references-count":9,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2004,10]]}},"alternative-id":["10.1002\/malq.200310118"],"URL":"https:\/\/doi.org\/10.1002\/malq.200310118","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,10]]}}}