{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T06:44:35Z","timestamp":1740120275506,"version":"3.37.3"},"reference-count":23,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"DOI":"10.13039\/501100000780","name":"European Union","doi-asserted-by":"crossref","award":["101071674"],"award-info":[{"award-number":["101071674"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"crossref"}]},{"name":"European Research Council","award":["771005"],"award-info":[{"award-number":["771005"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2023,6]]},"abstract":"<jats:p> We prove that there are continuum many clones on a three-element set even if they are considered up to homomorphic equivalence. The clones we use to prove this fact are clones consisting of self-dual operations, i.e. operations that preserve the relation [Formula: see text]. However, there are only countably many such clones when considered up to equivalence with respect to minor-preserving maps instead of clone homomorphisms. We give a full description of the set of clones of self-dual operations, ordered by the existence of minor-preserving maps. Our result can also be phrased as a statement about structures on a three-element set: we give a full description of the structures containing the relation [Formula: see text], ordered by primitive positive constructability, because there is a minor-preserving map from the polymorphism clone of a finite structure [Formula: see text] to the polymorphism clone of a finite structure [Formula: see text] if and only if there is a primitive positive construction of [Formula: see text] in [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218196723500327","type":"journal-article","created":{"date-parts":[[2023,5,4]],"date-time":"2023-05-04T13:42:49Z","timestamp":1683207769000},"page":"717-749","source":"Crossref","is-referenced-by-count":3,"title":["The lattice of clones of self-dual operations collapsed"],"prefix":"10.1142","volume":"33","author":[{"given":"Manuel","family":"Bodirsky","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Algebra, TU Dresden, Dresden, 01062, Germany"}]},{"given":"Albert","family":"Vucaj","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Algebra, TU Dresden, Dresden, 01062, Germany"}]},{"given":"Dmitriy","family":"Zhuk","sequence":"additional","affiliation":[{"name":"Department of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia"},{"name":"Department of Algebra, Faculty of Mathematics and Physics, Charles University, Prague, Czechia"}]}],"member":"219","published-online":{"date-parts":[[2023,6,8]]},"reference":[{"issue":"8","key":"S0218196723500327BIB001","doi-asserted-by":"crossref","first-page":"1673","DOI":"10.4171\/JEMS\/472","volume":"16","author":"Aichinger E.","year":"2014","journal-title":"J. Eur. Math. Soc."},{"issue":"1","key":"S0218196723500327BIB002","doi-asserted-by":"crossref","first-page":"3","DOI":"10.4153\/CJM-2011-087-3","volume":"65","author":"Barto L.","year":"2013","journal-title":"Can. J. Math."},{"issue":"1","key":"S0218196723500327BIB003","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1007\/s11856-017-1621-9","volume":"223","author":"Barto L.","year":"2018","journal-title":"Israel J. Math."},{"key":"S0218196723500327BIB004","series-title":"Lecture Notes in Logic","doi-asserted-by":"crossref","DOI":"10.1017\/9781107337534","volume-title":"Complexity of Infinite-Domain Constraint Satisfaction","volume":"52","author":"Bodirsky M.","year":"2021"},{"key":"S0218196723500327BIB005","doi-asserted-by":"crossref","first-page":"997","DOI":"10.1007\/s00493-022-4918-1","volume":"42","author":"Bodirsky M.","year":"2022","journal-title":"Combinatorica"},{"key":"S0218196723500327BIB006","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1007\/BF01070906","volume":"5","author":"Bodnar\u010duk V. G.","year":"1969","journal-title":"Cybernetics"},{"issue":"2","key":"S0218196723500327BIB008","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1016\/j.jcss.2015.07.004","volume":"82","author":"Bulatov A. A.","year":"2016","journal-title":"J. Comput. Syst. Sci."},{"key":"S0218196723500327BIB009","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1109\/FOCS.2017.37","volume-title":"58th IEEE Annual Symp. Foundations of Computer Science, FOCS 2017","author":"Bulatov A. A.","year":"2017"},{"key":"S0218196723500327BIB010","first-page":"227","volume":"6","author":"Cs\u00e1k\u00e1ny B.","year":"1984","journal-title":"Acta Cybern."},{"issue":"1","key":"S0218196723500327BIB011","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1007\/s00012-005-1924-2","volume":"54","author":"Cs\u00e1k\u00e1ny B.","year":"2005","journal-title":"Algeb. Univ."},{"key":"S0218196723500327BIB012","first-page":"8","volume":"23","author":"Demetrovics J.","year":"1979","journal-title":"MTA SzTAKI K\u00f6zlemenyek"},{"key":"S0218196723500327BIB013","first-page":"305","volume":"50","author":"Garcia O. C.","year":"1984","journal-title":"Mem. Amer. Math. Soc."},{"key":"S0218196723500327BIB014","doi-asserted-by":"crossref","first-page":"95","DOI":"10.2140\/pjm.1968.27.95","volume":"27","author":"Geiger D.","year":"1968","journal-title":"Pacific J. Math."},{"issue":"2","key":"S0218196723500327BIB015","first-page":"1153","volume":"95","author":"Jablonskij S. V.","year":"1954","journal-title":"Dokl. Akad. Nauk SSSR"},{"issue":"3","key":"S0218196723500327BIB016","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1007\/s00012-007-2012-6","volume":"56","author":"Larose B.","year":"2007","journal-title":"Algeb. Univ."},{"key":"S0218196723500327BIB017","series-title":"Springer Monographs in Mathematics","volume-title":"Function Algebras on Finite Sets: A Basic Course on Many-Valued Logic and Clone Theory\/Dietlinde Lau","author":"Lau D.","year":"2006"},{"key":"S0218196723500327BIB018","first-page":"261","volume":"40","author":"Marchenkov S. S.","year":"1983","journal-title":"Probl. Kibernetiki"},{"key":"S0218196723500327BIB019","volume-title":"The Two-Valued Iterative Systems of Mathematical Logic","volume":"5","author":"Post E. L.","year":"1941"},{"key":"S0218196723500327BIB020","first-page":"3817","volume":"260","author":"Rosenberg I. G.","year":"1965","journal-title":"C. R. Acad. Sci., Paris"},{"key":"S0218196723500327BIB021","first-page":"405","volume":"43","author":"Rosenberg I. G.","year":"1986","journal-title":"Lectures in Universal Algebra (Proc. Conf. Szeged, 1983), Colloq. Math. Soc. J. Bolyai"},{"key":"S0218196723500327BIB022","first-page":"44","volume":"127","author":"Yanov Y. I.","year":"1959","journal-title":"Dokl. Akad. Nauk SSS"},{"issue":"1","key":"S0218196723500327BIB023","first-page":"251","volume":"24","author":"Zhuk D. N.","year":"2015","journal-title":"J. Mult.-valued Log. Soft Comput."},{"key":"S0218196723500327BIB024","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1109\/FOCS.2017.38","volume-title":"58th IEEE Annual Symp. Foundations of Computer Science, FOCS 2017","author":"Zhuk D. N.","year":"2017"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196723500327","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,17]],"date-time":"2023-07-17T07:05:12Z","timestamp":1689577512000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0218196723500327"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6]]},"references-count":23,"journal-issue":{"issue":"04","published-print":{"date-parts":[[2023,6]]}},"alternative-id":["10.1142\/S0218196723500327"],"URL":"https:\/\/doi.org\/10.1142\/s0218196723500327","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"type":"print","value":"0218-1967"},{"type":"electronic","value":"1793-6500"}],"subject":[],"published":{"date-parts":[[2023,6]]}}}