{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,7]],"date-time":"2024-03-07T17:19:49Z","timestamp":1709831989211},"reference-count":19,"publisher":"Cambridge University Press (CUP)","issue":"8","license":[{"start":{"date-parts":[[2014,11,13]],"date-time":"2014-11-13T00:00:00Z","timestamp":1415836800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2015,12]]},"abstract":"<jats:p>In this paper, we develop a general framework for continuous data representations using positive predicate structures. We first show that basic principles of \u03a3-definability which are used to investigate computability, i.e., existence of a universal \u03a3-predicate and an algorithmic characterization of \u03a3-definability hold on all predicate structures without equality. Then we introduce positive predicate structures and show connections between these structures and effectively enumerable topological spaces. These links allow us to study computability over continuous data using logical and topological tools.<\/jats:p>","DOI":"10.1017\/s0960129513000315","type":"journal-article","created":{"date-parts":[[2014,11,13]],"date-time":"2014-11-13T23:39:31Z","timestamp":1415921971000},"page":"1669-1684","source":"Crossref","is-referenced-by-count":6,"title":["Positive predicate structures for continuous data"],"prefix":"10.1017","volume":"25","author":[{"given":"MARGARITA","family":"KOROVINA","sequence":"first","affiliation":[]},{"given":"OLEG","family":"KUDINOV","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,11,13]]},"reference":[{"key":"S0960129513000315_ref14","first-page":"427","article-title":"Abstract first order computability I, II","volume":"138","author":"Moschovakis","year":"1969","journal-title":"Transactions of the American Mathematical Society"},{"key":"S0960129513000315_ref17","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-45575-2_38"},{"key":"S0960129513000315_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-39813-4_21"},{"key":"S0960129513000315_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/11494645_30"},{"key":"S0960129513000315_ref4","volume-title":"Definability and Computability","author":"Ershov","year":"1996"},{"key":"S0960129513000315_ref11","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-73001-9_43"},{"key":"S0960129513000315_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(89)90036-5"},{"key":"S0960129513000315_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-45220-1_27"},{"key":"S0960129513000315_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-11035-5"},{"key":"S0960129513000315_ref16","doi-asserted-by":"crossref","first-page":"215","DOI":"10.4064\/fm-55-3-215-238","article-title":"Recursive metric spaces","volume":"55","author":"Moschovakis","year":"1976","journal-title":"Fundamenta Mathematicae"},{"key":"S0960129513000315_ref19","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-56999-9"},{"key":"S0960129513000315_ref18","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(93)90001-A"},{"key":"S0960129513000315_ref13","doi-asserted-by":"publisher","DOI":"10.1002\/malq.200710064"},{"key":"S0960129513000315_ref12","doi-asserted-by":"publisher","DOI":"10.1016\/j.entcs.2008.12.011"},{"key":"S0960129513000315_ref15","volume-title":"Elementary induction on abstract structures","author":"Moschovakis","year":"1974"},{"key":"S0960129513000315_ref5","first-page":"595","article-title":"Computable metrization","volume":"53","author":"Gr\u00fcbba","year":"2007","journal-title":"Mathematical Logic Quaterly"},{"key":"S0960129513000315_ref6","first-page":"43","article-title":"The meaning of specifications: Set-theoretical specification","volume":"5","author":"Hodges","year":"1993","journal-title":"Semantics of Programming Languages and Model Theory, Algebra, Logic and Applications Series"},{"key":"S0960129513000315_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0539-5"},{"key":"S0960129513000315_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(02)00693-X"}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129513000315","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,19]],"date-time":"2019-04-19T21:07:53Z","timestamp":1555708073000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129513000315\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,11,13]]},"references-count":19,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2015,12]]}},"alternative-id":["S0960129513000315"],"URL":"https:\/\/doi.org\/10.1017\/s0960129513000315","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,11,13]]}}}