{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,8,30]],"date-time":"2023-08-30T08:04:39Z","timestamp":1693382679699},"reference-count":7,"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":16956,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1967,10,9]]},"abstract":"<jats:p>It will be shown later in this paper that the class of all Hilbert spaces is not an elementary class (in the wider sense) in the lower predicate calculus. It is not difficult to find a type and a sentence in <jats:italic>L<jats:sub>\u03c91\u03c91<\/jats:sub><\/jats:italic> (of that type) whose models are precisely the Hilbert spaces (slightly altered to include in their domains the real or complex numbers).<\/jats:p>","DOI":"10.2307\/2270770","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T20:41:37Z","timestamp":1146948097000},"page":"295-304","source":"Crossref","is-referenced-by-count":5,"title":["The L<sub>\u03c91\u03c91<\/sub>-theory of hilbert spaces"],"prefix":"10.1017","volume":"32","author":[{"given":"Ralph","family":"Kopperman","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S002248120011299X_ref004","unstructured":"Kopperman R. , Application of infinitary languages to analysis, Doctoral Dissertation, M.I.T. Cambridge, Mass., 1965."},{"key":"S002248120011299X_ref003","article-title":"Completeness proof in predicate logic with infinitely long expressions","volume":"32","author":"Karp","year":"1967","journal-title":"this Journal"},{"key":"S002248120011299X_ref001","volume-title":"Linear operators","author":"Dunford","year":"1958"},{"key":"S002248120011299X_ref007","first-page":"81","article-title":"Arithmetic extensions of relational systems","volume":"13","author":"Tarski","year":"1957","journal-title":"Compositio Mathematicae,"},{"key":"S002248120011299X_ref002","unstructured":"Hanf W. , Some fundamental problems concerning languages with infinitely long expressions, Doctoral Dissertation, University of California, Berkeley, 1962."},{"key":"S002248120011299X_ref006","doi-asserted-by":"publisher","DOI":"10.4064\/cm-6-1-171-176"},{"key":"S002248120011299X_ref005","volume-title":"Complete theories","author":"Robinson","year":"1956"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S002248120011299X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T19:45:51Z","timestamp":1559504751000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002248120011299X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1967,10,9]]},"references-count":7,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1967,10,9]]}},"alternative-id":["S002248120011299X"],"URL":"https:\/\/doi.org\/10.2307\/2270770","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1967,10,9]]}}}