{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:54:55Z","timestamp":1760028895349,"version":"3.37.3"},"reference-count":13,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2020,4,1]],"date-time":"2020-04-01T00:00:00Z","timestamp":1585699200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/100000001","name":"NSF","doi-asserted-by":"publisher","award":["1600228"],"award-info":[{"award-number":["1600228"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science Committee of the Republic of Kazakhstan","award":["AP05131579"],"award-info":[{"award-number":["AP05131579"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,4,20]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>A computably enumerable equivalence relation (ceer) $X$ is called self-full if whenever $f$ is a reduction of $X$ to $X$, then the range of $f$ intersects all $X$-equivalence classes. It is known that the infinite self-full ceers properly contain the dark ceers, i.e. the infinite ceers which do not admit an infinite computably enumerable transversal. Unlike the collection of dark ceers, which are closed under the operation of uniform join, we answer a question from [ 4] by showing that there are self-full ceers $X$ and $Y$ so that their uniform join $X\\oplus Y$ is non-self-full. We then define and examine the hereditarily self-full ceers, which are the self-full ceers $X$ so that for any self-full $Y$, $X\\oplus Y$ is also self-full: we show that they are closed under uniform join and that every non-universal degree in ${\\operatorname{\\textbf{Ceers}}}_{\\operatorname{{\\mathcal{I}}}}$ have infinitely many incomparable hereditarily self-full strong minimal covers. In particular, every non-universal ceer is bounded by a hereditarily self-full ceer. Thus, the hereditarily self-full ceers form a properly intermediate class in between the dark ceers and the infinite self-full ceers, which is closed under $\\oplus $.<\/jats:p>","DOI":"10.1093\/logcom\/exaa023","type":"journal-article","created":{"date-parts":[[2020,3,6]],"date-time":"2020-03-06T12:26:17Z","timestamp":1583497577000},"page":"765-783","source":"Crossref","is-referenced-by-count":4,"title":["Self-full ceers and the uniform join operator"],"prefix":"10.1093","volume":"30","author":[{"given":"Uri","family":"Andrews","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Wisconsin\u2013Madison, WI 53706-1388, USA"}]},{"given":"Noah","family":"Schweber","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Wisconsin\u2013Madison, WI 53706-1388, USA"}]},{"given":"Andrea","family":"Sorbi","sequence":"first","affiliation":[{"name":"Dipartimento di Ingegneria Informatica e Scienze Matematiche, Universit\u00e0 Degli Studi di Siena, I-53100 Siena, Italy"}]}],"member":"286","published-online":{"date-parts":[[2020,4,22]]},"reference":[{"key":"2020050200393141000_ref1","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1007\/978-3-319-50062-1_25","article-title":"A survey on universal computably enumerable equivalence relations","volume-title":"Computability and Complexity. Essays Dedicated to Rodney G. Downey on the Occasion of His 60th Birthday","author":"Andrews","year":"2017"},{"key":"2020050200393141000_ref2","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1017\/jsl.2013.8","article-title":"Universal computably enumerable equivalence relations","volume":"74","author":"Andrews","year":"2014","journal-title":"Journal of Symbolic Logic"},{"journal-title":"Annals of Pure and Applied Logic","article-title":"The theory of ceers computes true arithmetic","author":"Andrews","key":"2020050200393141000_ref3"},{"key":"2020050200393141000_ref4","doi-asserted-by":"crossref","first-page":"193","DOI":"10.3233\/COM-180098","article-title":"Joins and meets in the structure of ceers","volume":"8","author":"Andrews","year":"2019","journal-title":"Computability"},{"key":"2020050200393141000_ref5","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1007\/BF02218645","article-title":"Positive equivalences","volume":"10","author":"Ershov","year":"1973","journal-title":"Algebra and Logic"},{"key":"2020050200393141000_ref6","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1002\/malq.19730191901","article-title":"Theorie der numerierungen I","volume":"19","author":"Ershov","year":"1973","journal-title":"Zeilachr. 1. Math. Logik und Grundlagen d. Math"},{"key":"2020050200393141000_ref7","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1002\/malq.19750210164","article-title":"Theorie der Numerierungen II","volume":"19","author":"Ershov","year":"1975","journal-title":"Zeilachr. 1. Math. Logik und Grundlagen d. Math"},{"key":"2020050200393141000_ref8","doi-asserted-by":"crossref","first-page":"122","DOI":"10.2178\/jsl\/1327068695","article-title":"Isomorphism relations on computable structures","volume":"77","author":"Fokina","year":"2012","journal-title":"The Journal of Symbolic Logic"},{"key":"2020050200393141000_ref9","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1017\/jsl.2015.11","article-title":"Linear orders realized by c.e. equivalence relations","volume":"81","author":"Fokina","year":"2016","journal-title":"The Journal of Symbolic Logic"},{"key":"2020050200393141000_ref10","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1023\/A:1010521410739","article-title":"Computably enumerable equivalence relations","volume":"67","author":"Gao","year":"2001","journal-title":"Studia Logica"},{"key":"2020050200393141000_ref11","doi-asserted-by":"crossref","first-page":"1263","DOI":"10.1016\/j.apal.2014.04.001","article-title":"Graphs realised by r.e. equivalence relations","volume":"165","author":"Gavruskin","year":"2014","journal-title":"Annals of Pure and Applied Logic"},{"volume-title":"On Group-Theoretic Decision Problems and Their Classification. (AM-68)","year":"1971","author":"Miller, III","key":"2020050200393141000_ref12"},{"key":"2020050200393141000_ref13","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1017\/S0960129516000335","article-title":"Calibrating word problems of groups via the complexity of equivalence relations","volume":"28","author":"Nies","year":"2018","journal-title":"Mathematical Structures in Computer Science"}],"container-title":["Journal of Logic and Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/logcom\/article-pdf\/30\/3\/765\/33154102\/exaa023.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/academic.oup.com\/logcom\/article-pdf\/30\/3\/765\/33154102\/exaa023.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,2]],"date-time":"2020-05-02T04:40:29Z","timestamp":1588394429000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/logcom\/article\/30\/3\/765\/5816092"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4]]},"references-count":13,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,4,22]]},"published-print":{"date-parts":[[2020,4,20]]}},"URL":"https:\/\/doi.org\/10.1093\/logcom\/exaa023","relation":{},"ISSN":["0955-792X","1465-363X"],"issn-type":[{"type":"print","value":"0955-792X"},{"type":"electronic","value":"1465-363X"}],"subject":[],"published-other":{"date-parts":[[2020,4]]},"published":{"date-parts":[[2020,4]]}}}