{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T10:17:58Z","timestamp":1775470678116,"version":"3.50.1"},"publisher-location":"Cham","reference-count":8,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783031643088","type":"print"},{"value":"9783031643095","type":"electronic"}],"license":[{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024]]},"DOI":"10.1007\/978-3-031-64309-5_22","type":"book-chapter","created":{"date-parts":[[2024,7,1]],"date-time":"2024-07-01T22:01:49Z","timestamp":1719871309000},"page":"277-284","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Hyperarithmetic Numerals"],"prefix":"10.1007","author":[{"given":"Caleb M. H.","family":"Camrud","sequence":"first","affiliation":[]},{"given":"Timothy H.","family":"McNicholl","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,7,2]]},"reference":[{"key":"22_CR1","volume-title":"Computable structures and the hyperarithmetical hierarchy, Studies in Logic and the Foundations of Mathematics","author":"CJ Ash","year":"2000","unstructured":"Ash, C.J., Knight, J.: Computable structures and the hyperarithmetical hierarchy, Studies in Logic and the Foundations of Mathematics, vol. 144. North-Holland Publishing Co., Amsterdam (2000)"},{"key":"22_CR2","doi-asserted-by":"crossref","unstructured":"Ben Yaacov, I., Usvyatsov, A.: Continuous first-order logic and local stability. Trans. Am. Math. Soc. 362, 5213\u20135259 (2010)","DOI":"10.1090\/S0002-9947-10-04837-3"},{"key":"22_CR3","doi-asserted-by":"crossref","unstructured":"Yaacov, I.B., Berenstein, A, Ward Henson, C., Usvyatsov, A.: Model theory for metric structures. Lond. Math. Soc. Lect. Note Ser. 350, 315\u2013427. Cambridge Univ. Press, Cambridge (2008). Model theory with applications to algebra and analysis. Vol. 2","DOI":"10.1017\/CBO9780511735219.011"},{"key":"22_CR4","doi-asserted-by":"crossref","unstructured":"Ben Yaacov, I., Iovino, J.: Model theoretic forcing in analysis. Ann. Pure Appl. Logic 158(3), 163\u2013174 (2009)","DOI":"10.1016\/j.apal.2007.10.011"},{"key":"22_CR5","doi-asserted-by":"crossref","unstructured":"Yaacov, I.B., Pedersen, A.P.: A proof of completeness for continuous first-order logic. J. Symb. Log. 75(1), 168\u2013190 (2010)","DOI":"10.2178\/jsl\/1264433914"},{"issue":"7","key":"22_CR6","doi-asserted-by":"publisher","first-page":"1111","DOI":"10.1007\/s00153-023-00884-4","volume":"62","author":"C Camrud","year":"2023","unstructured":"Camrud, C., Goldbring, I., McNicholl, T.H.: On the complexity of the theory of a computably presented metric structure. Arch. Math. Logic 62(7), 1111\u20131129 (2023)","journal-title":"Arch. Math. Logic"},{"key":"22_CR7","doi-asserted-by":"crossref","unstructured":"Eagle, C.J.: Expressive Power of Infinitary [0,1]-Logics, Beyond First Order Model Theory, pp. 3\u201322. CRC Press, Boca Raton, FL (2017)","DOI":"10.1201\/9781315368078-2"},{"key":"22_CR8","doi-asserted-by":"crossref","unstructured":"Sacks, G.E.: Higher recursion theory, Perspectives in Mathematical Logic. Springer-Verlag, Berlin (1990). MR1080970 (92a:03062)","DOI":"10.1007\/978-3-662-12013-2"}],"container-title":["Lecture Notes in Computer Science","Twenty Years of Theoretical and Practical Synergies"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-64309-5_22","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,1]],"date-time":"2024-07-01T22:03:42Z","timestamp":1719871422000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-64309-5_22"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024]]},"ISBN":["9783031643088","9783031643095"],"references-count":8,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-64309-5_22","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024]]},"assertion":[{"value":"2 July 2024","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"CiE","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Conference on Computability in Europe","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Amsterdam","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"The Netherlands","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2024","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"8 July 2024","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"12 July 2024","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"20","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"cie2024","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}