{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T09:51:39Z","timestamp":1648893099604},"reference-count":22,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2016,10,25]],"date-time":"2016-10-25T00:00:00Z","timestamp":1477353600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2017,3]]},"abstract":"Abstract<\/jats:title>A skeleton of the category with finite coproducts${\\cal D}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> freely generated by a single object has a subcategory isomorphic to a skeleton of the category with finite products ${\\cal C}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> freely generated by a countable set of objects. As a consequence, we obtain that ${\\cal D}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> has a subcategory equivalent with ${\\cal C}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. From a proof-theoretical point of view, this means that up to some identifications of formulae the deductions of pure conjunctive logic with a countable set of propositional letters can be represented by deductions in pure disjunctive logic with just one propositional letter. By taking opposite categories, one can replace coproduct by product, i.e., disjunction by conjunction, and the other way round, to obtain the dual results.<\/jats:p>","DOI":"10.1017\/s175502031600037x","type":"journal-article","created":{"date-parts":[[2016,10,25]],"date-time":"2016-10-25T02:29:31Z","timestamp":1477362571000},"page":"145-157","source":"Crossref","is-referenced-by-count":0,"title":["REPRESENTING CONJUNCTIVE DEDUCTIONS BY DISJUNCTIVE DEDUCTIONS"],"prefix":"10.1017","volume":"10","author":[{"given":"KOSTA","family":"DO\u0160EN","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ZORAN","family":"PETRI\u0106","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2016,10,25]]},"reference":[{"key":"S175502031600037X_ref2","doi-asserted-by":"publisher","DOI":"10.2307\/2589245"},{"key":"S175502031600037X_ref17","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1965-11234-4"},{"key":"S175502031600037X_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0073965"},{"key":"S175502031600037X_ref5","first-page":"149","volume-title":"Logic, Methodology and Philosophy of Science - Proceedings of the 14th International Congress (Nancy): Logic and Science Facing the New Technologies","author":"Do\u0161en","year":"2015"},{"key":"S175502031600037X_ref3","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-1207-1"},{"key":"S175502031600037X_ref4","first-page":"11","volume-title":"Third Mathematical Conference of the Republic of Srpska, Proceedings, Trebinje 2013, Zbornik radova","volume":"I","author":"Do\u0161en","year":"2014"},{"key":"S175502031600037X_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4049(96)00137-5"},{"key":"S175502031600037X_ref13","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0059557"},{"key":"S175502031600037X_ref19","first-page":"252","volume-title":"Aktual\u2019nye voprosy logiki i metodologii nauki","author":"Mints","year":"1980"},{"key":"S175502031600037X_ref7","doi-asserted-by":"publisher","DOI":"10.1002\/1521-3870(200101)47:1<137::AID-MALQ137>3.0.CO;2-F"},{"key":"S175502031600037X_ref8","doi-asserted-by":"publisher","DOI":"10.1002\/malq.200310063"},{"key":"S175502031600037X_ref18","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-9839-7"},{"key":"S175502031600037X_ref20","doi-asserted-by":"publisher","DOI":"10.1023\/A:1015186718090"},{"key":"S175502031600037X_ref21","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)70849-8"},{"key":"S175502031600037X_ref9","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1058448435"},{"key":"S175502031600037X_ref11","volume-title":"Proof-Net Categories","author":"Do\u0161en","year":"2007"},{"key":"S175502031600037X_ref12","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2012.10.008"},{"key":"S175502031600037X_ref22","volume-title":"Basic Proof Theory","author":"Troelstra","year":"1996"},{"key":"S175502031600037X_ref16","doi-asserted-by":"publisher","DOI":"10.1111\/j.1746-8361.1969.tb01194.x"},{"key":"S175502031600037X_ref6","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-22686-6_4"},{"key":"S175502031600037X_ref15","volume-title":"Introduction to Higher-Order Categorical Logic","author":"Lambek","year":"1986"},{"key":"S175502031600037X_ref10","volume-title":"Proof-Theoretical Coherence","author":"Do\u0161en","year":"2004"}],"container-title":["The Review of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S175502031600037X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,17]],"date-time":"2019-04-17T22:58:28Z","timestamp":1555541908000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S175502031600037X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,10,25]]},"references-count":22,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,3]]}},"alternative-id":["S175502031600037X"],"URL":"https:\/\/doi.org\/10.1017\/s175502031600037x","relation":{},"ISSN":["1755-0203","1755-0211"],"issn-type":[{"value":"1755-0203","type":"print"},{"value":"1755-0211","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,10,25]]}}}