{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,25]],"date-time":"2025-04-25T04:24:23Z","timestamp":1745555063967,"version":"3.40.4"},"reference-count":12,"publisher":"Springer Science and Business Media LLC","issue":"3-4","license":[{"start":{"date-parts":[[2024,12,6]],"date-time":"2024-12-06T00:00:00Z","timestamp":1733443200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,12,6]],"date-time":"2024-12-06T00:00:00Z","timestamp":1733443200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1500976"],"award-info":[{"award-number":["DMS-1500976"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Arch. Math. Logic"],"published-print":{"date-parts":[[2025,5]]},"DOI":"10.1007\/s00153-024-00954-1","type":"journal-article","created":{"date-parts":[[2024,12,6]],"date-time":"2024-12-06T21:40:26Z","timestamp":1733521226000},"page":"529-546","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Variations on the Feferman-Vaught theorem, with applications to $$\\prod _p \\mathbb {F}_p$$"],"prefix":"10.1007","volume":"64","author":[{"given":"Alice","family":"Medvedev","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2639-3474","authenticated-orcid":false,"given":"Alexander","family":"Van\u00a0Abel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,12,6]]},"reference":[{"issue":"2","key":"954_CR1","doi-asserted-by":"publisher","first-page":"239","DOI":"10.2307\/1970573","volume":"88","author":"J Ax","year":"1968","unstructured":"Ax, J.: The elementary theory of finite fields. Ann. Math. 88(2), 239\u2013271 (1968)","journal-title":"Ann. Math."},{"doi-asserted-by":"crossref","unstructured":"Burris, S.: Number theoretic density and logical limit laws. American Mathematical Society (2000)","key":"954_CR2","DOI":"10.1090\/surv\/086"},{"key":"954_CR3","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1016\/S0168-0072(97)00017-1","volume":"88","author":"Z Chatzidakis","year":"1997","unstructured":"Chatzidakis, Z.: Model theory of finite fields and pseudo-finite fields. Ann. Pure Appl. Logic 88, 95\u2013108 (1997)","journal-title":"Ann. Pure Appl. Logic"},{"issue":"3","key":"954_CR4","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2021.103074","volume":"173","author":"J Derakhshan","year":"2022","unstructured":"Derakhshan, J., Macintyre, A.: Model theory of adeles I. Ann. Pure Appl. Logic 173(3), 103074 (2022)","journal-title":"Ann. Pure Appl. Logic"},{"issue":"11","key":"954_CR5","doi-asserted-by":"publisher","first-page":"1639","DOI":"10.1016\/j.apal.2014.06.001","volume":"165","author":"J Derakhshan","year":"2013","unstructured":"Derakhshan, J., Macintyre, A.: Some supplements to Feferman-Vaught related to the model theory of Adeles. Ann. Pure Appl. Logic 165(11), 1639\u20131679 (2013)","journal-title":"Ann. Pure Appl. Logic"},{"key":"954_CR6","volume-title":"Abstract Algebra","author":"DS Dummit","year":"1991","unstructured":"Dummit, D.S., Foote, R.M.: Abstract Algebra. Prentice Hall, Hoboken (1991)"},{"issue":"2","key":"954_CR7","doi-asserted-by":"publisher","first-page":"57","DOI":"10.4064\/fm-47-1-57-103","volume":"47","author":"S Feferman","year":"1959","unstructured":"Feferman, S., Vaught, R.: The first order properties of products of algebraic systems. Fundam. Math. 47(2), 57\u2013103 (1959)","journal-title":"Fundam. Math."},{"key":"954_CR8","volume-title":"Introduction to Boolean Algebra","author":"S Givant","year":"2009","unstructured":"Givant, S., Halmos, P.: Introduction to Boolean Algebra. Springer-Verlag, New York (2009)"},{"key":"954_CR9","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511551574","volume-title":"Model Theory","author":"W Hodges","year":"1993","unstructured":"Hodges, W.: Model Theory. Cambridge University Press, Cambridge (1993)"},{"key":"954_CR10","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1090\/S0002-9947-1976-0422281-1","volume":"223","author":"C Kiefe","year":"1976","unstructured":"Kiefe, C.: Sets definable over finite fields: their Zeta functions. Trans. AMS 223, 45\u201359 (1976)","journal-title":"Trans. AMS"},{"key":"954_CR11","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-8622-1","volume-title":"A Course in Model Theory: An Introduction to Contemporary Mathematical Logic","author":"B Poizat","year":"2000","unstructured":"Poizat, B.: A Course in Model Theory: An Introduction to Contemporary Mathematical Logic. Springer, New York (2000)"},{"unstructured":"Weispfenning, V.: Model Theory of Lattice Products. Habilitation, Universitat Heidelberg (1978)","key":"954_CR12"}],"container-title":["Archive for Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-024-00954-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00153-024-00954-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-024-00954-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,25]],"date-time":"2025-04-25T02:58:27Z","timestamp":1745549907000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00153-024-00954-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,6]]},"references-count":12,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2025,5]]}},"alternative-id":["954"],"URL":"https:\/\/doi.org\/10.1007\/s00153-024-00954-1","relation":{},"ISSN":["0933-5846","1432-0665"],"issn-type":[{"type":"print","value":"0933-5846"},{"type":"electronic","value":"1432-0665"}],"subject":[],"published":{"date-parts":[[2024,12,6]]},"assertion":[{"value":"15 February 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 October 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 December 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}