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{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,12]],"date-time":"2024-09-12T09:01:49Z","timestamp":1726131709805},"reference-count":26,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2019,5,3]],"date-time":"2019-05-03T00:00:00Z","timestamp":1556841600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2021,3]]},"abstract":"Abstract<\/jats:title>It is known that a countable \n

\n$\\omega $\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-categorical structure interprets all finite structures primitively positively if and only if its polymorphism clone maps to the clone of projections on a two-element set via a continuous clone homomorphism. We investigate the relationship between the existence of a clone homomorphism to the projection clone, and the existence of such a homomorphism which is continuous and thus meets the above criterion.<\/jats:p>","DOI":"10.1017\/jsl.2019.23","type":"journal-article","created":{"date-parts":[[2019,5,3]],"date-time":"2019-05-03T05:58:21Z","timestamp":1556863101000},"page":"148-161","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":19,"title":["PROJECTIVE CLONE HOMOMORPHISMS"],"prefix":"10.1017","volume":"86","author":[{"given":"MANUEL","family":"BODIRSKY","sequence":"first","affiliation":[]},{"given":"MICHAEL","family":"PINSKER","sequence":"additional","affiliation":[]},{"given":"ANDR\u00c1S","family":"PONGR\u00c1CZ","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2019,5,3]]},"reference":[{"key":"S0022481219000239_r12","doi-asserted-by":"publisher","DOI":"10.1137\/16M1082974"},{"key":"S0022481219000239_r8","doi-asserted-by":"publisher","DOI":"10.1109\/LICS.2010.13"},{"key":"S0022481219000239_r11","doi-asserted-by":"publisher","DOI":"10.1109\/LICS.2019.8785883"},{"key":"S0022481219000239_r15","doi-asserted-by":"publisher","DOI":"10.1145\/2764899"},{"key":"S0022481219000239_r24","volume-title":"Annals of Mathematics Studies","volume":"5","author":"Post","year":"1941"},{"key":"S0022481219000239_r14","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-014-1042-y"},{"key":"S0022481219000239_r22","volume-title":"A Shorter Model Theory","author":"Hodges","year":"1997"},{"key":"S0022481219000239_r2","doi-asserted-by":"crossref","unstructured":"[2] Barto, L. , Kompatscher, M. , Ol\u0161\u00e1k, M. , Van Pham, T. , and Pinsker, M. , Equations in oligomorphic clones and the constraint satisfaction problem for omega-categorical structures . 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