{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T10:05:36Z","timestamp":1649153136244},"reference-count":4,"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":17998,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1964,12]]},"abstract":"<jats:p>This is really a note to Wajsberg's [4].<\/jats:p><jats:p>In [3] J. C. C. McKinsey proved the following two completeness theorems: (1) theorem 6: <jats:italic>If A is a wff of S2 with just r (proper or improper) sub-wffs, then A is provable in S2 iff A is satisfied by every normal S2-matrix with no more than 2<jats:sup>2r+1<\/jats:sup> elements<\/jats:italic>; (2) theorem 13: <jats:italic>if A is a wff of<\/jats:italic> S4 <jats:italic>with just r sub-wffs, then A is provable in S4 iff A is satisfied by every normal S4-matrix with no more than 2<jats:sup>2r<\/jats:sup> elements.<\/jats:italic> Now, a similar theorem has not been explicitly formulated for S5, even though a similar, even simpler, theorem has been almost at hand since Wajsberg's [4] was published in 1933, namely:<\/jats:p><jats:p>Theorem. <jats:italic>If A is a wff of S5 with just n propositional variables, then A is provable in S5 iff A is satisfied by a normal SS-matrix with 2<jats:sup>2n<\/jats:sup> elements<\/jats:italic>.<\/jats:p>","DOI":"10.2307\/2270373","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T20:26:14Z","timestamp":1146947174000},"page":"191-192","source":"Crossref","is-referenced-by-count":1,"title":["A note on S5"],"prefix":"10.1017","volume":"29","author":[{"given":"Hector-Neri","family":"Castaneda","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S002248120011583X_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/BF01708856"},{"key":"S002248120011583X_ref003","first-page":"117","volume":"6","author":"Mckinsey","year":"1941","journal-title":"A solution of the decision problem for the Lewis systems S2 and S4, with an application to topology"},{"key":"S002248120011583X_ref001","volume-title":"Introduction to Mathematical Logic","volume":"1","author":"Church","year":"1956"},{"key":"S002248120011583X_ref002","first-page":"150","volume":"5","author":"Dugundji","year":"1940","journal-title":"Note on a property of matrices for Lewis and Langford's calculi of propositions"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S002248120011583X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,3]],"date-time":"2019-06-03T20:05:51Z","timestamp":1559592351000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002248120011583X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1964,12]]},"references-count":4,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1964,12]]}},"alternative-id":["S002248120011583X"],"URL":"https:\/\/doi.org\/10.2307\/2270373","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1964,12]]}}}