{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T02:01:25Z","timestamp":1648778485677},"reference-count":11,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":12520,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1979,12]]},"abstract":"Metakides and Nerode in [2] suggested the study of what they termed the lattice of recursively enumerable substructures of a recursively presented model. For example, Metakides and Nerode in [3] introduced the lattice of of recusively enumerable subspaces, , of a recursively presented vector space V<\/jats:italic>\u221e<\/jats:sub>. The similarities and differences between and \u2130, the lattice of recursively enumerable subsets of the natural numbers N<\/jats:italic> as defined in [9], have been studied by Metakides and Nerode, Kalantari, Remmel, Retzlaff, and Shore. In [6], we studied some similarities and differences between \u2130 and the lattice of recursively enumerable sub-algebras of a weakly recursively presented Boolean algebra and this paper continues that study. A weakly recursively presented Boolean algebra (W.R.P.B.A.)<\/jats:italic>, , consists of a recursive subset of N<\/jats:italic>, \u2223\u2223, called the field of , and operations (meet), (join), and (complement) which are partial recursive and under which becomes a Boolean algebra. We shall write and for the zero and unit of . If S<\/jats:italic> is a subset of , we let (S<\/jats:italic>)* denote the subalgebra generated by S<\/jats:italic>. Given sub-algebras B<\/jats:italic> and C<\/jats:italic> of , we let B<\/jats:italic> + C<\/jats:italic> denote (B<\/jats:italic> \u22c3 C<\/jats:italic>)*. A subalgebra B<\/jats:italic> of is recursively enumerable (recursive) if {x<\/jats:italic> \u2208 \u2223\u2223 x<\/jats:italic> \u2208 B<\/jats:italic>} is a recursively enumerable (recursive) subset of \u2223\u2223. The set of all recursively enumerable subalgebras of , , forms a lattice under the operations of intersection and sum (+).<\/jats:p>","DOI":"10.2307\/2273292","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T17:51:21Z","timestamp":1146937881000},"page":"533-548","source":"Crossref","is-referenced-by-count":6,"title":["R<\/i>-maximal Boolean algebras"],"prefix":"10.1017","volume":"44","author":[{"given":"J. B.","family":"Remmel","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200048416_ref004","author":"Metakides","journal-title":"Recursion theory on orderings"},{"key":"S0022481200048416_ref010","volume-title":"Boolean algebras","author":"Sikorski","year":"1964"},{"key":"S0022481200048416_ref006","volume-title":"Annals of Mathematical Logic","author":"Remmel"},{"key":"S0022481200048416_ref002","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1007\/BFb0062858","volume-title":"Algebra and logic, Lecture Notes in Mathematics","author":"Metakides","year":"1975"},{"key":"S0022481200048416_ref005","volume-title":"Algebra Universalis","author":"Remmel"},{"key":"S0022481200048416_ref011","unstructured":"Vaught R. L. , Topics in the theory of arithmetical classes and Boolean algebras, Ph.D. Thesis, University of California, Berkeley, 1954."},{"key":"S0022481200048416_ref007","first-page":"430","volume":"43","author":"Remmel","year":"1978","journal-title":"A r-maximal vector space not contained in any maximal vector space"},{"key":"S0022481200048416_ref001","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1968-0227009-1"},{"key":"S0022481200048416_ref008","first-page":"162","volume":"32","author":"Robinson","year":"1967","journal-title":"Simplicity of recursively enumerable sets"},{"key":"S0022481200048416_ref003","volume-title":"Annals of Mathematical Logic","author":"Metakides"},{"key":"S0022481200048416_ref009","volume-title":"Theory of recursive functions and effective computability","author":"Rogers","year":"1967"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200048416","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,26]],"date-time":"2019-05-26T16:28:08Z","timestamp":1558888088000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200048416\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1979,12]]},"references-count":11,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1979,12]]}},"alternative-id":["S0022481200048416"],"URL":"https:\/\/doi.org\/10.2307\/2273292","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1979,12]]}}}