{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T01:52:35Z","timestamp":1778809955336,"version":"3.51.4"},"reference-count":5,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":3238,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1998,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper it is shown that addition of certain reductions to the standard cut removing reductions of deductions in prepositional logic makes prepositional logic non\u2010normalizable. From this follows that some provable propositions in prepositional logic has no direct proof.<\/jats:p>","DOI":"10.1002\/malq.19980440105","type":"journal-article","created":{"date-parts":[[2007,5,31]],"date-time":"2007-05-31T04:00:27Z","timestamp":1180584027000},"page":"69-91","source":"Crossref","is-referenced-by-count":14,"title":["Propositions in Prepositional Logic Provable Only by Indirect Proofs"],"prefix":"10.1002","volume":"44","author":[{"given":"Jan","family":"Ekman","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01201353"},{"key":"e_1_2_1_2_3","volume-title":"The Collected Papers of Gerhard Gentzen","author":"Szabo M. E.","year":"1969"},{"key":"e_1_2_1_3_2","volume-title":"Natural Deduction: A Proof\u2010Theoretical Study","author":"Prawitz D.","year":"1964"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)70849-8"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.2307\/2274910"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19980440105","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19980440105","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,28]],"date-time":"2023-10-28T12:55:03Z","timestamp":1698497703000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19980440105"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,1]]},"references-count":5,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1998,1]]}},"alternative-id":["10.1002\/malq.19980440105"],"URL":"https:\/\/doi.org\/10.1002\/malq.19980440105","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,1]]}}}