{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T10:49:07Z","timestamp":1775472547175,"version":"3.50.1"},"reference-count":15,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":15167,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1972,9]]},"abstract":"<jats:p>The main result of this paper is the following transfer theorem: <jats:italic>If T is an elementary theory which has a \u03ba-like model where \u03ba is hyperinaccessible of type \u03c9, then T has a \u03bb-like model for each \u03bb<\/jats:italic> &gt; card(<jats:italic>T<\/jats:italic>). Helling [3] obtained the same conclusion under the stronger hypothesis that <jats:italic>\u03ba<\/jats:italic> is weakly compact. Fuhrken conjectured in [1] that the same conclusion would result if <jats:italic>\u03ba<\/jats:italic> were merely inaccessible. (He also showed there the connection with a problem about generalized quantifiers.) Thus, our theorem lies properly between Helling's theorem and Fuhrken's conjecture. In [9] it is shown that this theorem is actually the best possible. This theorem and the other results of this paper were announced by the authors in [10].<\/jats:p><jats:p>In \u00a71 we prove as Theorem 1 a slightly stronger form of the above theorem. This theorem is generalized in \u00a72 to Theorem 2 which concerns theories which permit the omitting of types. The methods used in \u00a7\u00a71 and 2 are also applicable to problems regarding Hanf numbers as well as to two-cardinal problems.<\/jats:p>","DOI":"10.2307\/2272739","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:17:55Z","timestamp":1146950275000},"page":"531-537","source":"Crossref","is-referenced-by-count":13,"title":["On power-like models for hyperinaccessible cardinals"],"prefix":"10.1017","volume":"37","author":[{"given":"James H.","family":"Schmerl","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Saharon","family":"Shelah","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200079081_ref015","first-page":"390","volume-title":"The theory of models","author":"Vaught","year":"1965"},{"key":"S0022481200079081_ref013","first-page":"964","article-title":"Model-theoretic proof of a partition theorem","volume":"17","author":"Simpson","year":"1970","journal-title":"Notices of the American Mathematical Society"},{"key":"S0022481200079081_ref010","first-page":"840","article-title":"On models with orderings","volume":"16","author":"Schmerl","year":"1969","journal-title":"Notices of the American Mathematical Society"},{"key":"S0022481200079081_ref009","first-page":"521","volume":"37","author":"Schmerl","year":"1972","journal-title":"An elementary sentence which has ordered models"},{"key":"S0022481200079081_ref008","unstructured":"Schmerl J. H. , On \u03ba-like models for inaccessible \u03ba. Doctoral Dissertation, University of California, Berkeley, 1971."},{"key":"S0022481200079081_ref006","first-page":"265","volume-title":"The theory of models","author":"Morley","year":"1965"},{"key":"S0022481200079081_ref005","first-page":"257","volume-title":"Infinitistic methods","author":"Macdowell","year":"1961"},{"key":"S0022481200079081_ref004","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1960.10.223"},{"key":"S0022481200079081_ref003","unstructured":"Helling M. , Model-theoretic problems for some extentions of first-order languages, Doctoral Dissertation, University of California, Berkeley, 1966."},{"key":"S0022481200079081_ref001","first-page":"121","volume-title":"The theory of models","author":"Fuhrken","year":"1965"},{"key":"S0022481200079081_ref007","first-page":"43","volume-title":"Symposia mathematica","volume":"V","author":"Morley","year":"1971"},{"key":"S0022481200079081_ref012","first-page":"247","volume":"37","author":"Shelah","year":"1972","journal-title":"On models with power-like orderings"},{"key":"S0022481200079081_ref011","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1970.34.541"},{"key":"S0022481200079081_ref014","doi-asserted-by":"publisher","DOI":"10.4064\/fm-54-3-303-304"},{"key":"S0022481200079081_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)71505-2"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200079081","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,30]],"date-time":"2019-05-30T20:57:32Z","timestamp":1559249852000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200079081\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1972,9]]},"references-count":15,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1972,9]]}},"alternative-id":["S0022481200079081"],"URL":"https:\/\/doi.org\/10.2307\/2272739","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1972,9]]}}}