{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T11:17:52Z","timestamp":1648639072619},"reference-count":14,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":11424,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1982,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Two real-valued deduction schemes are introduced, which agree on \u22a2 \u22bf but not on \u0393 \u22a2 \u22bf, where \u0393 and \u22a2 are finite sets of formulae. Using the first scheme we axiomatize real-valued equality so that it induces metrics on the domains of appropriate structures. We use the second scheme to reduce substitutivity of equals to uniform continuity, with respect to the metric equality, of interpretations of predicates in structures. This continuity extends from predicates to arbitrary formulae and the appropriate models have completions resembling analytic completions of metric spaces. We provide inference rules for the two deductions and discuss definability of each of them by means of the other.<\/jats:p>","DOI":"10.2307\/2273098","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:01:43Z","timestamp":1146938503000},"page":"772-792","source":"Crossref","is-referenced-by-count":14,"title":["Real-valued models with metric equality and uniformly continuous predicates"],"prefix":"10.1017","volume":"47","author":[{"given":"Michael","family":"Katz","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200043668_ref009","first-page":"175","volume-title":"Proceedings of the 11th International Symposium on Multiple-Valued Logic","author":"Katz","year":"1981"},{"key":"S0022481200043668_ref012","volume-title":"Lectures on Boolean-valued models of set theory","author":"Scott","year":"1967"},{"key":"S0022481200043668_ref014","first-page":"188","volume-title":"Proceedings of the Tarski Symposium","volume":"25","author":"Scott","year":"1974"},{"key":"S0022481200043668_ref010","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(71)90017-9"},{"key":"S0022481200043668_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-7373(76)80003-X"},{"key":"S0022481200043668_ref001","first-page":"43","volume":"28","author":"Belluce","year":"1963","journal-title":"A weak completeness theorem for infinite valued predicate logic"},{"key":"S0022481200043668_ref002","first-page":"74","article-title":"A new proof of the completeness of the \u0141ukasiewicz axioms","volume":"93","author":"Chang","year":"1959","journal-title":"Transactions of the American Mathematical Society"},{"key":"S0022481200043668_ref003","volume-title":"The logic of sheaves","author":"Fourman","year":"1974"},{"key":"S0022481200043668_ref004","first-page":"399","article-title":"A non-classical logic for physics","volume":"33","author":"Giles","year":"1974","journal-title":"Stadia Logica"},{"key":"S0022481200043668_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/BF00485654"},{"key":"S0022481200043668_ref007","first-page":"77","volume":"28","author":"Hay","year":"1963","journal-title":"Axiomatization of the infinite valued predicate calculus"},{"key":"S0022481200043668_ref008","volume-title":"\u0141ukasiewicz logic and the foundations of measurement","author":"Katz","year":"1979"},{"key":"S0022481200043668_ref011","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1958-0094299-1"},{"key":"S0022481200043668_ref013","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)71542-8"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200043668","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,24]],"date-time":"2019-05-24T16:18:26Z","timestamp":1558714706000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200043668\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1982,12]]},"references-count":14,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1982,12]]}},"alternative-id":["S0022481200043668"],"URL":"https:\/\/doi.org\/10.2307\/2273098","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1982,12]]}}}