{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T02:36:57Z","timestamp":1774924617486,"version":"3.50.1"},"reference-count":13,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,1,15]],"date-time":"2014-01-15T00:00:00Z","timestamp":1389744000000},"content-version":"unspecified","delay-in-days":5524,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bull. symb. log."],"published-print":{"date-parts":[[1998,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A way is found to add axioms to sequent calculi that maintains the eliminability of cut, through the representation of axioms as rules of inference of a suitable form. By this method, the structural analysis of proofs is extended from pure logic to free-variable theories, covering all classical theories, and a wide class of constructive theories. All results are proved for systems in which also the rules of weakening and contraction can be eliminated. Applications include a system of predicate logic with equality in which also cuts on the equality axioms are eliminated.<\/jats:p>","DOI":"10.2307\/420956","type":"journal-article","created":{"date-parts":[[2006,5,7]],"date-time":"2006-05-07T03:12:02Z","timestamp":1146971522000},"page":"418-435","source":"Crossref","is-referenced-by-count":87,"title":["Cut Elimination in the Presence of Axioms"],"prefix":"10.1017","volume":"4","author":[{"given":"Sara","family":"Negri","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jan","family":"von Plato","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,1,15]]},"reference":[{"key":"S1079898600007149_ref012","volume-title":"Basic proof theory","author":"Troelstra","year":"1996"},{"key":"S1079898600007149_ref007","volume-title":"Proof theory and logical complexity","author":"Girard","year":"1987"},{"key":"S1079898600007149_ref005","first-page":"19","article-title":"Neue Fassung des Widerspruchsfreiheitsbeweises f\u00fcr die reine Zahlentheorie","volume":"4","author":"Gentzen","year":"1938","journal-title":"Forschungen zur Logik und zur Grundlegung der exakten Wissenschaften"},{"key":"S1079898600007149_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/BF01201363"},{"key":"S1079898600007149_ref011","unstructured":"von Plato J. , On the proof theory of classical logic, submitted, 1998."},{"key":"S1079898600007149_ref009","article-title":"Untersuchungen zum Pr\u00e4dikatenkalk\u00fcl","volume":"I","author":"Ketonen","year":"1944","journal-title":"Annales Academiae Scientiarum Fennicae, Series A"},{"key":"S1079898600007149_ref006","volume-title":"The collected papers of Gerhard Gentzen","author":"Gentzen","year":"1969"},{"key":"S1079898600007149_ref002","doi-asserted-by":"crossref","DOI":"10.1090\/mmono\/067","volume-title":"Mathematical intuitionism: Introduction to proof theory","author":"Dragalin","year":"1988"},{"key":"S1079898600007149_ref003","volume-title":"Research Report CS\/97\/8","author":"Dyckhoff","year":"1997"},{"key":"S1079898600007149_ref010","volume-title":"Archive for Mathematical Logic","author":"Negri"},{"key":"S1079898600007149_ref013","first-page":"453","volume-title":"Logic colloquium '84","author":"Uesu","year":"1104"},{"key":"S1079898600007149_ref008","doi-asserted-by":"publisher","DOI":"10.1093\/logcom\/1.2.261"},{"key":"S1079898600007149_ref001","article-title":"Review of Ketonen [9]","volume":"10","author":"Bernays","year":"1945","journal-title":"Journal"}],"container-title":["Bulletin of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1079898600007149","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,10]],"date-time":"2019-05-10T15:48:51Z","timestamp":1557503331000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1079898600007149\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,12]]},"references-count":13,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1998,12]]}},"alternative-id":["S1079898600007149"],"URL":"https:\/\/doi.org\/10.2307\/420956","relation":{},"ISSN":["1079-8986","1943-5894"],"issn-type":[{"value":"1079-8986","type":"print"},{"value":"1943-5894","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,12]]}}}