{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T08:06:00Z","timestamp":1775462760313,"version":"3.50.1"},"reference-count":18,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2012,5]]},"abstract":"<jats:p> A quasivariety is a universal Horn class of algebraic structures containing the trivial structure. The set [Formula: see text] of all subquasivarieties of a quasivariety [Formula: see text] forms a complete lattice under inclusion. A lattice isomorphic to [Formula: see text] for some quasivariety [Formula: see text] is called a lattice of quasivarieties or a quasivariety lattice. The Birkhoff\u2013Maltsev Problem asks which lattices are isomorphic to lattices of quasivarieties. A lattice L is called unreasonable if the set of all finite sublattices of L is not computable, that is, there is no algorithm for deciding whether a finite lattice is a sublattice of L. The main result of this paper states that for any signature \u03c3 containing at least one non-constant operation, there is a quasivariety [Formula: see text] of signature \u03c3 such that the quasivariety lattice [Formula: see text] is unreasonable. Moreover, there are uncountable unreasonable lattices of quasivarieties. We also present some corollaries of the main result. <\/jats:p>","DOI":"10.1142\/s0218196711006728","type":"journal-article","created":{"date-parts":[[2011,8,11]],"date-time":"2011-08-11T01:38:15Z","timestamp":1313026695000},"page":"1250006","source":"Crossref","is-referenced-by-count":8,"title":["UNREASONABLE LATTICES OF QUASIVARIETIES"],"prefix":"10.1142","volume":"22","author":[{"given":"A. M.","family":"NURAKUNOV","sequence":"first","affiliation":[{"name":"Institute of Mathematics of the National Academy of Sciences, Chui pr. 265a, Bishkek 720071, Kyrgyzstan"},{"name":"Eurasian Mathematical Institute of the Eurasian National University, Munaitpasov Str. 5, Astana 010008, Kazakhastan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,5,6]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-005-7378-x"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00970904"},{"key":"rf5","volume-title":"Universal Algebra","author":"Cohn P. M.","year":"1965"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/BF01188380"},{"key":"rf7","first-page":"52","volume":"46","author":"Dziobiak W.","journal-title":"Ruch Filozoficzny"},{"key":"rf8","first-page":"436","volume":"15","author":"Gorbunov V. A.","journal-title":"Algebra Logic"},{"key":"rf9","volume-title":"Algebraic Theory of Quasivarieties","author":"Gorbunov V. A.","year":"1998"},{"key":"rf10","first-page":"12","volume":"2","author":"Gorbunov V. A.","journal-title":"Trudy Inst. Math. Sibirsk. Otdel. Akad. Nauk. SSSR"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-1973-100-4"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1007\/s10587-005-0053-6"},{"key":"rf14","first-page":"7","volume":"27","author":"Kartashov V. K.","journal-title":"Math. Notes"},{"key":"rf15","first-page":"49","volume":"26","author":"Kartashov V. K.","journal-title":"Siberian Math. J."},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1007\/BF01221791"},{"key":"rf18","volume-title":"Algebraic Systems","author":"Maltsev A. I.","year":"1973"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-005-3320-5"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196796000040"},{"key":"rf21","first-page":"283","volume":"40","author":"Nurakunov A. M.","journal-title":"Algebra Logic"},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.1007\/s00012-007-2036-y"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196711006728","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T20:03:20Z","timestamp":1565121800000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196711006728"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,5]]},"references-count":18,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2012,5,6]]},"published-print":{"date-parts":[[2012,5]]}},"alternative-id":["10.1142\/S0218196711006728"],"URL":"https:\/\/doi.org\/10.1142\/s0218196711006728","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,5]]}}}