{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,4]],"date-time":"2023-09-04T10:40:39Z","timestamp":1693824039702},"reference-count":5,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2021,1,16]],"date-time":"2021-01-16T00:00:00Z","timestamp":1610755200000},"content-version":"vor","delay-in-days":46,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2020,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We determine the number of non\u2010isomorphic semi\u2010Heyting algebras on an <jats:italic>n<\/jats:italic>\u2010element chain, where <jats:italic>n<\/jats:italic> is a positive integer, using a recursive method. We then prove that the numbers obtained agree with those determined in [1]. We apply the formula to calculate the number of non\u2010isomorphic semi\u2010Heyting chains of a given size in some important subvarieties of the variety of semi\u2010Heyting algebras that were introduced in\u00a0[5]. We further exploit this recursive method to calculate the numbers  of non\u2010isomorphic semi\u2010Heyting chains with <jats:italic>n<\/jats:italic> elements such that removing the <jats:italic>m<\/jats:italic>th element () we are left with a subalgebra. We also solve a related problem posed in [1] of determining the number of ways a semi\u2010Heyting chain with  elements can be extended to a <jats:italic>n<\/jats:italic> element semi\u2010Heyting chain by adding a new element in the <jats:italic>m<\/jats:italic>th place. Finally we combine these results by finding a second way to calculate the numbers  that provides some extra\u00a0information.<\/jats:p>","DOI":"10.1002\/malq.201900070","type":"journal-article","created":{"date-parts":[[2021,1,16]],"date-time":"2021-01-16T09:11:37Z","timestamp":1610788297000},"page":"409-417","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A note on chain\u2010based semi\u2010Heyting algebras"],"prefix":"10.1002","volume":"66","author":[{"given":"Juan Manuel","family":"Cornejo","sequence":"first","affiliation":[{"name":"Instituto de Matem\u00e1tica de Bah\u00eda Blanca Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas Avenida Leandro N. Alem 1253 Bah\u00eda Blanca Argentina"},{"name":"Departamento de Matem\u00e1tica Universidad Nacional del Sur Avenida Leandro N. Alem 1253 Bah\u00eda Blanca Argentina"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luiz F.","family":"Monteiro","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica Universidad Nacional del Sur Avenida Leandro N. Alem 1253 Bah\u00eda Blanca Argentina"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hanamantagouda P.","family":"Sankappanavar","sequence":"additional","affiliation":[{"name":"Department of Mathematics State University of New York 1 Hawk Drive New Paltz NY 12561 United States of America"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ignacio D.","family":"Viglizzo","sequence":"additional","affiliation":[{"name":"Instituto de Matem\u00e1tica de Bah\u00eda Blanca Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas Avenida Leandro N. Alem 1253 Bah\u00eda Blanca Argentina"},{"name":"Departamento de Matem\u00e1tica Universidad Nacional del Sur Avenida Leandro N. Alem 1253 Bah\u00eda Blanca Argentina"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2021,1,16]]},"reference":[{"key":"e_1_2_6_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-010-0604-0"},{"key":"e_1_2_6_3_1","volume-title":"Distributive lattices","author":"Balbes R.","year":"1974"},{"key":"e_1_2_6_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-0208(08)73814-3"},{"key":"e_1_2_6_5_1","volume-title":"An Algebraic Approach to Non\u2010classical Logics","author":"Rasiowa H.","year":"1974"},{"key":"e_1_2_6_6_1","first-page":"33","volume-title":"Actas del IX Congreso Dr. Antonio A. R. Monteiro held in Bah\u00eda Blanca","author":"Sankappanavar H. P.","year":"2008"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.201900070","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/malq.201900070","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.201900070","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,3]],"date-time":"2023-09-03T16:33:16Z","timestamp":1693758796000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.201900070"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12]]},"references-count":5,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2020,12]]}},"alternative-id":["10.1002\/malq.201900070"],"URL":"https:\/\/doi.org\/10.1002\/malq.201900070","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,12]]},"assertion":[{"value":"2019-10-03","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2020-03-12","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-01-16","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}