{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,5,23]],"date-time":"2022-05-23T13:11:10Z","timestamp":1653311470324},"reference-count":5,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2021,6,8]],"date-time":"2021-06-08T00:00:00Z","timestamp":1623110400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,5,21]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Combinatorial operations on sets are almost never well defined on Turing degrees, a fact so obvious that counterexamples are worth exhibiting. The case we focus on is the symmetric-difference operator; there are pairs of (nonzero) degrees for which the symmetric-difference operation is well defined. Some examples can be extracted from the literature, e.g. from the existence of nonzero degrees with strong minimal covers. We focus on the case of incomparable r.e. degrees for which the symmetric-difference operation is well defined.<\/jats:p>","DOI":"10.1093\/jigpal\/jzab017","type":"journal-article","created":{"date-parts":[[2021,4,16]],"date-time":"2021-04-16T21:57:06Z","timestamp":1618610226000},"page":"499-518","source":"Crossref","is-referenced-by-count":0,"title":["Computability and the Symmetric Difference Operator"],"prefix":"10.1093","volume":"30","author":[{"given":"Uri","family":"Andrews","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Wisconsin, Madison, WI 53706-1325, USA"}]},{"given":"Peter M","family":"Gerdes","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Mathematics and Science Center, Room 368, Oakland University, 146 Library Drive, Rochester, MI 48309-4479, USA"}]},{"given":"Steffen","family":"Lempp","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Wisconsin, Madison, WI 53706-1325, USA"}]},{"given":"Joseph S","family":"Miller","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Wisconsin, Madison, WI 53706-1325, USA"}]},{"given":"Noah D","family":"Schweber","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Wisconsin, Madison, WI 53706-1325, USA"}]}],"member":"286","published-online":{"date-parts":[[2021,6,8]]},"reference":[{"key":"2022052312313767200_ref1","doi-asserted-by":"crossref","first-page":"527","DOI":"10.2307\/2274867","article-title":"The strong anticupping property for recursively enumerable degrees","volume":"54","author":"Cooper","year":"1989","journal-title":"Journal of Symbolic Logic"},{"key":"2022052312313767200_ref2","volume-title":"Degrees of Unsolvability","author":"Sacks","year":"1963"},{"key":"2022052312313767200_ref3","doi-asserted-by":"crossref","first-page":"160","DOI":"10.2307\/2275022","article-title":"Complementation in the Turing degrees","volume":"54","author":"Slaman","year":"1989","journal-title":"Journal of Symbolic Logic"},{"key":"2022052312313767200_ref4","volume-title":"Classical recursion theory. Vol. II","author":"Odifreddi","year":"1999"},{"key":"2022052312313767200_ref5","article-title":"Perspectives in Mathematical Logic","volume-title":"Recursively Enumerable Sets and Degrees","author":"Soare","year":"1987"}],"container-title":["Logic Journal of the IGPL"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/jigpal\/article-pdf\/30\/3\/499\/43781586\/jzab017.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jigpal\/article-pdf\/30\/3\/499\/43781586\/jzab017.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,23]],"date-time":"2022-05-23T12:31:53Z","timestamp":1653309113000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jigpal\/article\/30\/3\/499\/6291047"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,8]]},"references-count":5,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2021,6,8]]},"published-print":{"date-parts":[[2022,5,21]]}},"URL":"https:\/\/doi.org\/10.1093\/jigpal\/jzab017","relation":{},"ISSN":["1367-0751","1368-9894"],"issn-type":[{"value":"1367-0751","type":"print"},{"value":"1368-9894","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2022,6]]},"published":{"date-parts":[[2021,6,8]]}}}