{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,12,10]],"date-time":"2023-12-10T17:38:13Z","timestamp":1702229893098},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2002,10,21]],"date-time":"2002-10-21T00:00:00Z","timestamp":1035158400000},"content-version":"unspecified","delay-in-days":20,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2002,10]]},"abstract":"A categorical framework for equational logics is presented, together with axiomatizability \nresults in the style of Birkhoff. The distinctive categorical structures used are inclusion \nsystems, which are an alternative to factorization systems in which factorization is required \nto be unique rather than unique \u2018up to an isomorphism\u2019. In this framework, models are any \nobjects, and equations are special epimorphisms in [Cfr ], while satisfaction is injectivity. A first \nresult says that equations-as-epimorphisms define exactly the quasi-varieties, suggesting that \nepimorphisms actually represent conditional equations. In fact, it is shown that the \nprojectivity\/freeness of the domain of epimorphisms is what makes the difference between \nunconditional and conditional equations, the first defining the varieties, as expected. An \nabstract version of the axiom of choice seems to be sufficient for free objects to be \nprojective, in which case the definitional power of equations of projective and free domain, \nrespectively, is the same. Connections with other abstract formulations of equational logics \nare investigated, together with an organization of our logic as an institution.<\/jats:p>","DOI":"10.1017\/s0960129501003474","type":"journal-article","created":{"date-parts":[[2002,10,30]],"date-time":"2002-10-30T11:46:10Z","timestamp":1035978370000},"page":"541-563","source":"Crossref","is-referenced-by-count":9,"title":["Axiomatizability in inclusive equational logics"],"prefix":"10.1017","volume":"12","author":[{"given":"GRIGORE","family":"RO\u015eU","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2002,10,21]]},"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129501003474","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,7]],"date-time":"2019-05-07T00:31:11Z","timestamp":1557189071000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129501003474\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,10]]},"references-count":0,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2002,10]]}},"alternative-id":["S0960129501003474"],"URL":"https:\/\/doi.org\/10.1017\/s0960129501003474","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,10]]}}}