{"id":"https://openalex.org/W1582757356","doi":"https://doi.org/10.2307/2274647","title":"The ordertype of <i>\u03b2</i>-R.E. sets","display_name":"The ordertype of <i>\u03b2</i>-R.E. sets","publication_year":1990,"publication_date":"1990-06-01","ids":{"openalex":"https://openalex.org/W1582757356","doi":"https://doi.org/10.2307/2274647","mag":"1582757356"},"language":"en","primary_location":{"id":"doi:10.2307/2274647","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2274647","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033022989","display_name":"Klaus Sutner","orcid":null},"institutions":[{"id":"https://openalex.org/I108468826","display_name":"Stevens Institute of Technology","ror":"https://ror.org/02z43xh36","country_code":"US","type":"education","lineage":["https://openalex.org/I108468826"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Klaus Sutner","raw_affiliation_strings":["Stevens Institute of Technology, Hoboken, New Jersey 07030","Stevens Inst of Tech"],"affiliations":[{"raw_affiliation_string":"Stevens Institute of Technology, Hoboken, New Jersey 07030","institution_ids":["https://openalex.org/I108468826"]},{"raw_affiliation_string":"Stevens Inst of Tech","institution_ids":["https://openalex.org/I108468826"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5033022989"],"corresponding_institution_ids":["https://openalex.org/I108468826"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06390503,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"55","issue":"2","first_page":"573","last_page":"576"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.709949254989624},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.6677492260932922},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5444546341896057},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.4812183678150177},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4732830226421356},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.4731755554676056},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.45660096406936646},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4446815848350525},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13759014010429382},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13349014520645142},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09559309482574463}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.709949254989624},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.6677492260932922},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5444546341896057},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.4812183678150177},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4732830226421356},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.4731755554676056},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.45660096406936646},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4446815848350525},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13759014010429382},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13349014520645142},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09559309482574463},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2307/2274647","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2274647","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W568910110","https://openalex.org/W2002453609","https://openalex.org/W2014445098","https://openalex.org/W2025499500","https://openalex.org/W2069839261","https://openalex.org/W2149022879","https://openalex.org/W2330191353","https://openalex.org/W6702236459"],"related_works":["https://openalex.org/W2590472383","https://openalex.org/W2383873009","https://openalex.org/W2393580911","https://openalex.org/W2212184297","https://openalex.org/W3207130397","https://openalex.org/W3156456913","https://openalex.org/W2390945180","https://openalex.org/W2394052932","https://openalex.org/W2350360626","https://openalex.org/W2142539551"],"abstract_inverted_index":{"Abstract":[0],"Let":[1],"\u03b2":[2,9,18,22,55,67,75],"be":[3],"an":[4],"arbitrary":[5],"limit":[6],"ordinal.":[7],"A":[8],"-r.e.":[10,19,56],"set":[11,57],"is":[12,58],"l":[13,25,46,59],"-finite":[14,26,47,60],"iff":[15,61],"all":[16],"its":[17],"subsets":[20],"are":[21],"-recursive.":[23],"The":[24],"sets":[27,34,48],"correspond":[28],"to":[29],"the":[30,36,69],"ideal":[31],"of":[32,38,45,51,74],"finite":[33],"in":[35,49],"lattice":[37],"r.e.":[39],"sets.":[40],"We":[41],"give":[42],"a":[43,54],"characterization":[44],"terms":[50],"their":[52],"ordertype:":[53],"it":[62],"has":[63],"ordertype":[64],"less":[65],"than":[66],"*,":[68],"\u03a3":[70],"1":[71],",":[72],"projectum":[73],").":[76]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}