{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,29]],"date-time":"2023-10-29T04:38:35Z","timestamp":1698554315698},"reference-count":12,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":3238,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1998,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Continuing the paper [7], in which the Blum\u2010Shub\u2010Smale approach to computability over the reals has been generalized to arbitrary algebraic structures, this paper deals with computability and recognizability over structures of infinite signature. It begins with discussing related properties of the linear and scalar real structures and of their discrete counterparts over the natural numbers. Then the existence of universal functions is shown to be equivalent to the effective encodability of the underlying structure. Such structures even have universal functions satisfying the s\u2010m\u2010n theorem and related features. The real and discrete examples are discussed with respect to effective encodability. Megiddo structures and computational extensions of effectively encodable structures are encodable, too. As further variants of universality, universal functions with enumerable sets of program codes and such ones with constructible codes are investigated. Finally, the existence of m\u2010complete sets is shown to be independent of the effective encodability of structures, and the linear and scalar structures are discussed once more, under this aspect.<\/jats:p>","DOI":"10.1002\/malq.19980440311","type":"journal-article","created":{"date-parts":[[2007,5,31]],"date-time":"2007-05-31T08:19:48Z","timestamp":1180599588000},"page":"394-416","source":"Crossref","is-referenced-by-count":2,"title":["Computability Over Structures of Infinite Signature"],"prefix":"10.1002","volume":"44","author":[{"given":"Armin","family":"Hemmerling","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0701-6"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-1989-15750-9"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1006\/jcom.1995.1018"},{"key":"e_1_2_1_5_2","volume-title":"Berechnungstheorie f\u00fcr Informatiker","author":"Engeler E.","year":"1988"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1006\/jcom.1997.0444"},{"key":"e_1_2_1_7_2","volume-title":"Computability of string functions over algebraic structures","author":"Hemmerling A."},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19980440102"},{"key":"e_1_2_1_9_2","first-page":"36","article-title":"Computing over the reals with addition and order","volume":"133","author":"Koiran P.","year":"1994","journal-title":"J. Theor. Comput. Sc."},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/0885-064X(92)90007-X"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1006\/jcom.1993.1023"},{"key":"e_1_2_1_12_2","first-page":"113","article-title":"A survey on real structural complexity theory","volume":"3","author":"Meer K.","year":"1996","journal-title":"Bull. Belg. Math. Soc."},{"key":"e_1_2_1_13_2","first-page":"432","volume-title":"From Topology to Computation: Proceedings of the Smalefest","author":"Megiddo N.","year":"1993"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19980440311","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19980440311","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,29]],"date-time":"2023-10-29T00:49:49Z","timestamp":1698540589000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19980440311"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,1]]},"references-count":12,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1998,1]]}},"alternative-id":["10.1002\/malq.19980440311"],"URL":"https:\/\/doi.org\/10.1002\/malq.19980440311","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,1]]}}}