{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,21]],"date-time":"2025-06-21T04:07:12Z","timestamp":1750478832022,"version":"3.41.0"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2002,8,6]],"date-time":"2002-08-06T00:00:00Z","timestamp":1028592000000},"content-version":"unspecified","delay-in-days":66,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2002,6]]},"abstract":"<jats:p>This work is a step toward the development of a logic for types and computation that \nincludes not only the usual spaces of mathematics and constructions, but also spaces from \nlogic and domain theory. Using realizability, we investigate a configuration of three toposes \nthat we regard as describing a notion of relative computability. Attention is focussed on a \ncertain local map of toposes, which we first study axiomatically, and then by deriving a \nmodal calculus as its internal logic. The resulting framework is intended as a setting for the \nlogical and categorical study of relative computability.<\/jats:p>","DOI":"10.1017\/s0960129502003675","type":"journal-article","created":{"date-parts":[[2002,9,11]],"date-time":"2002-09-11T15:09:02Z","timestamp":1031756942000},"page":"319-334","source":"Crossref","is-referenced-by-count":7,"title":["Local realizability toposes and a modal logic for computability"],"prefix":"10.1017","volume":"12","author":[{"given":"STEVEN","family":"AWODEY","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"LARS","family":"BIRKEDAL","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"DANA S.","family":"SCOTT","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2002,8,6]]},"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129502003675","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,20]],"date-time":"2025-06-20T22:11:45Z","timestamp":1750457505000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129502003675\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,6]]},"references-count":0,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2002,4]]}},"alternative-id":["S0960129502003675"],"URL":"https:\/\/doi.org\/10.1017\/s0960129502003675","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"type":"print","value":"0960-1295"},{"type":"electronic","value":"1469-8072"}],"subject":[],"published":{"date-parts":[[2002,6]]}}}