{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T13:12:54Z","timestamp":1778764374684,"version":"3.51.4"},"reference-count":0,"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":8867,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1989,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In a modal system of arithmetic, a theory <jats:italic>S<\/jats:italic> has the modal disjunction property if whenever <jats:italic>S<\/jats:italic> \u22a2 \u25a1<jats:italic>\u03c6<\/jats:italic> \u2228 \u25a1<jats:italic>\u03c8<\/jats:italic>, either <jats:italic>S<\/jats:italic> \u22a2 \u25a1<jats:italic>\u03c6<\/jats:italic> or <jats:italic>S<\/jats:italic> \u22a2 \u25a1<jats:italic>\u03c8<\/jats:italic>. <jats:italic>S<\/jats:italic> has the modal numerical existence property if whenever <jats:italic>S<\/jats:italic> \u22a2 \u2203<jats:italic>x<\/jats:italic> \u25a1<jats:italic>\u03c6<\/jats:italic>(<jats:italic>x<\/jats:italic>), there is some natural number <jats:italic>n<\/jats:italic> such that <jats:italic>S<\/jats:italic> \u22a2 \u25a1<jats:italic>\u03c6<\/jats:italic>(<jats:bold>n<\/jats:bold>). Under certain broadly applicable assumptions, these two properties are equivalent.<\/jats:p>","DOI":"10.2307\/2274825","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:32:43Z","timestamp":1146954763000},"page":"1456-1459","source":"Crossref","is-referenced-by-count":5,"title":["The equivalence of the disjunction and existence properties for modal arithmetic"],"prefix":"10.1017","volume":"54","author":[{"given":"Harvey","family":"Friedman","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"Sheard","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200041190","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,22]],"date-time":"2023-03-22T10:33:40Z","timestamp":1679481220000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200041190\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989,12]]},"references-count":0,"aliases":["10.1017\/s0022481200041190"],"journal-issue":{"issue":"4","published-print":{"date-parts":[[1989,12]]}},"alternative-id":["S0022481200041190"],"URL":"https:\/\/doi.org\/10.2307\/2274825","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1989,12]]}}}