{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T14:19:44Z","timestamp":1775053184197,"version":"3.50.1"},"reference-count":22,"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":6767,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1995,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A. M.Pitts in [Pi] proved that <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200018351_inline1\"\/> is a bi-Heyting category satisfying the Lawvere condition. We show that the embedding \u03a6: <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200018351_inline1\"\/> \u2192 <jats:italic>Sh<\/jats:italic>(<jats:bold>P<jats:sub>0<\/jats:sub><\/jats:bold>, <jats:bold>J<jats:sub>0<\/jats:sub><\/jats:bold>) into the topos of sheaves, (<jats:bold>P<jats:sub>0<\/jats:sub><\/jats:bold> is the category of finite rooted posets and open maps, <jats:bold>J<jats:sub>0<\/jats:sub><\/jats:bold> the canonical topology on <jats:bold>P<jats:sub>0<\/jats:sub><\/jats:bold>) given by <jats:italic>H<\/jats:italic> \u21a6 <jats:italic>HA<\/jats:italic>(<jats:italic>H<\/jats:italic>, <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200018351_inline2\"\/>(\u2212)) : <jats:bold>P<jats:sub>0<\/jats:sub><\/jats:bold> \u2192 Set preserves the structure mentioned above, finite coproducts, and subobject classifier; it is also conservative. This whole structure on <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200018351_inline1\"\/> can be derived from that of <jats:italic>Sh<\/jats:italic>(<jats:bold>P<jats:sub>0<\/jats:sub><\/jats:bold>, <jats:bold>J<jats:sub>0<\/jats:sub><\/jats:bold>) via the embedding \u03a6. We also show that the equivalence relations in <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200018351_inline1\"\/> are not effective in general. On the way to these results we establish a new kind of duality between <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200018351_inline1\"\/> and a category of sheaves equipped with certain structure defined in terms of Ehrenfeucht games. Our methods are model-theoretic and combinatorial as opposed to proof-theoretic as in [Pi].<\/jats:p>","DOI":"10.2307\/2275765","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:56:10Z","timestamp":1146941770000},"page":"911-939","source":"Crossref","is-referenced-by-count":33,"title":["A sheaf representation and duality for finitely presented Heyting algebras"],"prefix":"10.1017","volume":"60","author":[{"given":"Silvio","family":"Ghilardi","sequence":"first","affiliation":[]},{"given":"Marek","family":"Zawadowski","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200018351_ref013","volume-title":"Duality and definability in first order logic","volume":"503","author":"Makkai","year":"1993"},{"key":"S0022481200018351_ref022","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(94)00018-X"},{"key":"S0022481200018351_ref001","volume-title":"S\u00e9minaire de g\u00e9om\u00e9trie alg\u00e9brique 4","author":"Artin","year":"1972"},{"key":"S0022481200018351_ref016","first-page":"33","volume":"57","author":"Pitts","year":"1992","journal-title":"On an interpretation of second order quantification in first order intuitionistic propositional logic"},{"key":"S0022481200018351_ref020","doi-asserted-by":"publisher","DOI":"10.1007\/BF02945107"},{"key":"S0022481200018351_ref010","volume-title":"Stone spaces","author":"Johnstone","year":"1982"},{"key":"S0022481200018351_ref002","first-page":"152","volume":"51","author":"Bellissima","year":"1986","journal-title":"Finitely generatedfree Hey ting algebras"},{"key":"S0022481200018351_ref004","first-page":"619","volume":"50","author":"Fine","year":"1985","journal-title":"Logics containing K4, Part II"},{"key":"S0022481200018351_ref015","volume-title":"Completenessresultsfor intuitionistic and modal logic in a categorical setting","author":"Reyes","year":"1992"},{"key":"S0022481200018351_ref003","first-page":"31","volume":"34","author":"Fine","year":"1974","journal-title":"Logics containing K4, Part I"},{"key":"S0022481200018351_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-2977-2"},{"key":"S0022481200018351_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0059396"},{"key":"S0022481200018351_ref007","first-page":"240","volume-title":"Mathematical Reports of Academy of Sciences of Canada","volume":"XIV","author":"Ghilardi","year":"1992"},{"key":"S0022481200018351_ref008","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(93)E0084-2"},{"key":"S0022481200018351_ref009","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093635330"},{"key":"S0022481200018351_ref011","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0084226"},{"key":"S0022481200018351_ref012","volume-title":"Categories for the working mathematician","author":"MacLane","year":"1971"},{"key":"S0022481200018351_ref014","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0066201"},{"key":"S0022481200018351_ref018","first-page":"42","article-title":"Admissibility of inference rules with parameters in intuitionistic logic and intuitionistic Kripke models","volume":"312","author":"Rybakov","year":"1990","journal-title":"Doklady Akademii Nauk"},{"key":"S0022481200018351_ref017","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/2.2.186"},{"key":"S0022481200018351_ref019","volume-title":"Dissertationesmathematicae","volume":"CCCXXIII","author":"Shavrukov","year":"1993"},{"key":"S0022481200018351_ref021","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-5203-4_4"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200018351","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,13]],"date-time":"2019-05-13T17:13:30Z","timestamp":1557767610000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200018351\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,9]]},"references-count":22,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1995,9]]}},"alternative-id":["S0022481200018351"],"URL":"https:\/\/doi.org\/10.2307\/2275765","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,9]]}}}