{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T01:13:05Z","timestamp":1725498785804},"reference-count":5,"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":19916,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1959,9]]},"abstract":"<jats:p>The system of sentential calculus presented below has peculiarities which may be of some interest. It is complete in the sense that every classical (two-valued) tautology is provable. In spite of this it is not Post complete (nor is it absolutely complete), i.e., one can add to the system an unprovable formula without proving a sentential variable as a theorem (or without making every formula a theorem). Thus the system may be extended by adjoining an unprovable formula without making the system inconsistent in the Post (or in absolute) sense. There are many distinct extensions of this kind. For every formula \u03b1<jats:sub>1<\/jats:sub> that is not a theorem and which adjoined to the system does not make the system Post (or absolutely) inconsistent there is a formula \u03b1<jats:sub>2<\/jats:sub> such that adjunction of \u03b1<jats:sub>2<\/jats:sub> to the original system leaves \u03b1<jats:sub>1<\/jats:sub> unprovable.<\/jats:p>","DOI":"10.2307\/2963776","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T20:05:21Z","timestamp":1146945921000},"page":"193-202","source":"Crossref","is-referenced-by-count":13,"title":["Extendible sentential calculus"],"prefix":"10.1017","volume":"24","author":[{"given":"H.","family":"Hiz","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200123412_ref005","doi-asserted-by":"publisher","DOI":"10.4064\/cm-2-3-4-236-240"},{"key":"S0022481200123412_ref002","volume-title":"Recherches sur la d\u00e9duction logique","author":"Gentzen","year":"1955"},{"key":"S0022481200123412_ref003","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100033120"},{"key":"S0022481200123412_ref001","volume":"I","author":"Church","year":"1956","journal-title":"Introduction to mathematical logic"},{"key":"S0022481200123412_ref004","first-page":"34","article-title":"Extendible sentential calculus","volume":"5","author":"Hi\u017c","year":"1958","journal-title":"Notices of the American Mathematical Society"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200123412","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,5]],"date-time":"2019-06-05T19:59:45Z","timestamp":1559764785000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200123412\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1959,9]]},"references-count":5,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1959,9]]}},"alternative-id":["S0022481200123412"],"URL":"https:\/\/doi.org\/10.2307\/2963776","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1959,9]]}}}