{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T12:38:48Z","timestamp":1740141528457,"version":"3.37.3"},"reference-count":9,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2020,12,22]],"date-time":"2020-12-22T00:00:00Z","timestamp":1608595200000},"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":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1928930"],"award-info":[{"award-number":["DMS-1928930"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,1,22]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We investigate the computability of algebraic closure and definable closure with respect to a collection of formulas. We show that for a computable collection of formulas of quantifier rank at most $n$, in any given computable structure, both algebraic and definable closure with respect to that collection are $\\varSigma ^0_{n+2}$ sets. We further show that these bounds are tight.<\/jats:p>","DOI":"10.1093\/logcom\/exaa070","type":"journal-article","created":{"date-parts":[[2020,12,7]],"date-time":"2020-12-07T23:46:50Z","timestamp":1607384810000},"page":"2-19","source":"Crossref","is-referenced-by-count":0,"title":["On computable aspects of algebraic and definable closure"],"prefix":"10.1093","volume":"31","author":[{"given":"Nathanael","family":"Ackerman","sequence":"first","affiliation":[{"name":"Harvard University, Cambridge, MA 02138, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cameron","family":"Freer","sequence":"additional","affiliation":[{"name":"Massachusetts Institute of Technology, Cambridge, MA 02139, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rehana","family":"Patel","sequence":"additional","affiliation":[{"name":"African Institute for Mathematical Sciences, M\u2019bour\u2013Thi\u00e8s, Senegal"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2020,12,23]]},"reference":[{"key":"2021122301015626200_ref1","doi-asserted-by":"crossref","DOI":"10.1017\/fms.2016.15","article-title":"Invariant measures concentrated on countable structures","volume":"4","author":"Ackerman","year":"2016","journal-title":"Forum of Mathematics, Sigma"},{"key":"2021122301015626200_ref2","first-page":"1","article-title":"Computability of algebraic and definable closure","volume-title":"LFCS 2020: Logical Foundations of Computer Science","author":"Ackerman","year":"2020"},{"key":"2021122301015626200_ref3","doi-asserted-by":"crossref","first-page":"454","DOI":"10.1006\/aama.1998.0641","article-title":"Universal graphs with forbidden subgraphs and algebraic closure","volume":"22","author":"Cherlin","year":"1999","journal-title":"Advances in Applied Mathematics"},{"key":"2021122301015626200_ref4","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1017\/CBO9781107338579.006","article-title":"Computable model theory","volume-title":"Turing\u2019s Legacy: Developments from Turing\u2019s Ideas in Logic","author":"Fokina","year":"2014"},{"key":"2021122301015626200_ref5","first-page":"3","article-title":"Pure computable model theory","volume-title":"Handbook of Recursive Mathematics","author":"Harizanov","year":"1998"},{"key":"2021122301015626200_ref6","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511551574","volume-title":"Model theory","author":"Hodges","year":"1993"},{"key":"2021122301015626200_ref7","doi-asserted-by":"crossref","first-page":"2525","DOI":"10.5802\/aif.3071","article-title":"Algebraic and definable closure in free groups","volume":"66","author":"Ould Houcine","year":"2016","journal-title":"Annales de l\u2019institut Fourier (Grenoble)"},{"key":"2021122301015626200_ref8","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-31933-4","volume-title":"Turing computability","author":"Soare","year":"2016"},{"key":"2021122301015626200_ref9","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139015417","volume-title":"A course in model theory","author":"Tent","year":"2012"}],"container-title":["Journal of Logic and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/logcom\/article-pdf\/31\/1\/2\/36677521\/exaa070.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/logcom\/article-pdf\/31\/1\/2\/36677521\/exaa070.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,12,23]],"date-time":"2021-12-23T01:02:14Z","timestamp":1640221334000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/logcom\/article\/31\/1\/2\/6044463"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,23]]},"references-count":9,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,12,23]]},"published-print":{"date-parts":[[2021,1,22]]}},"URL":"https:\/\/doi.org\/10.1093\/logcom\/exaa070","relation":{},"ISSN":["0955-792X","1465-363X"],"issn-type":[{"type":"print","value":"0955-792X"},{"type":"electronic","value":"1465-363X"}],"subject":[],"published-other":{"date-parts":[[2021,1]]},"published":{"date-parts":[[2020,12,23]]}}}