{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T20:13:34Z","timestamp":1776888814618,"version":"3.51.2"},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":8593,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1990,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The paper proves a predicate version of Solovay's well-known theorem on provability interpretations of modal logic:<\/jats:p><jats:p><jats:italic>If a closed modal predicate-logical formula R is not valid in some finite Kripke model, then there exists an arithmetical interpretation f such that PA<\/jats:italic> \u22ac <jats:italic>fR<\/jats:italic>.<\/jats:p><jats:p>This result implies the arithmetical completeness of arithmetically correct modal predicate logics with the finite model property (including the one-variable fragments of <jats:italic>QGL<\/jats:italic> and <jats:italic>QS<\/jats:italic>). The proof was obtained by adding \u201cthe predicate part\u201d as a specific addition to the standard Solovay construction.<\/jats:p>","DOI":"10.2307\/2274475","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:36:50Z","timestamp":1146955010000},"page":"1090-1098","source":"Crossref","is-referenced-by-count":16,"title":["Finite Kripke models and predicate logics of provability"],"prefix":"10.1017","volume":"55","author":[{"given":"Sergei","family":"Artemov","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Giorgie","family":"Dzhaparidze","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200025573_ref010","first-page":"521","article-title":"On effective predicate logics of provability","volume":"297","author":"Artemov","year":"1987","journal-title":"Doklady Akademii Nauk SSSR"},{"key":"S0022481200025573_ref009","first-page":"46","volume-title":"Complexity of calculations and algorithms","author":"Vardanyan","year":"1988"},{"key":"S0022481200025573_ref008","first-page":"11","article-title":"Arithmetic complexity of predicate logics of provability and their fragments","volume":"288","author":"Vardanyan","year":"1986","journal-title":"Doklady Akademii Nauk SSSR"},{"key":"S0022481200025573_ref007","first-page":"165","volume":"52","author":"Boolos","year":"1987","journal-title":"The degree of the set of predicate provability logics that are true under every interpretation"},{"key":"S0022481200025573_ref005","first-page":"270","article-title":"Nonarithmeticity of truth predicate logics of provability","volume":"284","author":"Artemov","year":"1985","journal-title":"Doklady Akademii Nauk SSSR"},{"key":"S0022481200025573_ref004","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093870577"},{"key":"S0022481200025573_ref001","first-page":"39","article-title":"Eine Interpretation des intuitionistischen Aussagenkalk\u00fcls","volume":"4","author":"G\u00f6del","year":"1933","journal-title":"Ergebnisse eines Mathematischen Kolloquiums"},{"key":"S0022481200025573_ref011","doi-asserted-by":"publisher","DOI":"10.1007\/BF01708856"},{"key":"S0022481200025573_ref012","first-page":"265","article-title":"Arithmetical completeness of provability logics with quantifier modalities","volume":"132","author":"Dzhaparidze","year":"1988","journal-title":"Soobshcheniya Akademii Nauk Gruzinsko\u012d SSR"},{"key":"S0022481200025573_ref003","volume-title":"The unprovability of consistency: an essay in modal logic","author":"Boolos","year":"1979"},{"key":"S0022481200025573_ref006","first-page":"5","volume-title":"Complexity of calculations and algorithms","author":"Artemov","year":"1988"},{"key":"S0022481200025573_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/BF02757006"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200025573","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,18]],"date-time":"2019-05-18T20:25:38Z","timestamp":1558211138000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200025573\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,9]]},"references-count":12,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1990,9]]}},"alternative-id":["S0022481200025573"],"URL":"https:\/\/doi.org\/10.2307\/2274475","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,9]]}}}