{"id":"https://openalex.org/W2029974361","doi":"https://doi.org/10.2307/2274662","title":"Boolean algebras and orbits of the lattice of r.e sets modulo the finite sets","display_name":"Boolean algebras and orbits of the lattice of r.e sets modulo the finite sets","publication_year":1990,"publication_date":"1990-06-01","ids":{"openalex":"https://openalex.org/W2029974361","doi":"https://doi.org/10.2307/2274662","mag":"2029974361"},"language":"en","primary_location":{"id":"doi:10.2307/2274662","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2274662","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/A5062882161","display_name":"Peter Cholak","orcid":null},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Peter Cholak","raw_affiliation_strings":["Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706","Department of Mathematics , University of Wisconsin , Madison, Wisconsin, 53706"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706","institution_ids":["https://openalex.org/I135310074"]},{"raw_affiliation_string":"Department of Mathematics , University of Wisconsin , Madison, Wisconsin, 53706","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5062882161"],"corresponding_institution_ids":["https://openalex.org/I135310074"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.16374112,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"55","issue":"2","first_page":"744","last_page":"760"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998000264167786,"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":0.9995999932289124,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.8092008829116821},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7318606972694397},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.6349204778671265},{"id":"https://openalex.org/keywords/orbit","display_name":"Orbit (dynamics)","score":0.5971461534500122},{"id":"https://openalex.org/keywords/automorphism-group","display_name":"Automorphism group","score":0.5785909295082092},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.4945783317089081},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4886656105518341},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.45311108231544495},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.426277756690979},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.381264328956604},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1312098205089569},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0856354832649231}],"concepts":[{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.8092008829116821},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7318606972694397},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.6349204778671265},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.5971461534500122},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.5785909295082092},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.4945783317089081},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4886656105518341},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.45311108231544495},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.426277756690979},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.381264328956604},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1312098205089569},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0856354832649231},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2274662","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2274662","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"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183743329","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183743329","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1975466840","https://openalex.org/W2049442092","https://openalex.org/W2056414301","https://openalex.org/W2062249564","https://openalex.org/W2127316662","https://openalex.org/W2315181607","https://openalex.org/W4232277851"],"related_works":["https://openalex.org/W2072365522","https://openalex.org/W2951152791","https://openalex.org/W4307786893","https://openalex.org/W4302155387","https://openalex.org/W2949256963","https://openalex.org/W2545189445","https://openalex.org/W2115024785","https://openalex.org/W2949890955","https://openalex.org/W2085781584","https://openalex.org/W4289596368"],"abstract_inverted_index":{"An":[0],"important":[1],"program":[2],"in":[3,79,273],"the":[4,7,9,18,21,27,66,80,92,214,226,268,293,302],"study":[5],"of":[6,11,20,30,57,68,71,82,94,162,271,295],"structure":[8],"lattice":[10],"r.e.":[12,249],"sets":[13,216,228,308],"modulo":[14],"finite":[15],"sets,":[16],"is":[17,53,115,138,145,159,174,178,192,238,248,267,298],"classification":[19],"orbits":[22],"under":[23,181],"Aut":[24,35,60,72,105,182,196],"(":[25,36,62,73,107,183,198],"),":[26],"automorphism":[28],"group":[29],",":[31,85],"If":[32,102,157],"\u03a6":[33,103,114,194],"\u2208":[34,49,100,104,190,195,288],")":[37,42,63,74,108,184,199,203,254,266,278],"and":[38,129,133,149,164,185,222,250],"\u03a6(":[39,201],"W":[40,44,167],"e":[41,48],"=*":[43,204],"h(e)":[45],"for":[46,87,98,186],"all":[47,187],"\u03c9,":[50],"then":[51,109,143,173],"h":[52],"called":[54],"a":[55,77,139,146,160,193,218,258,312],"presentation":[56,78],"\u03a6.":[58],"Define":[59],"\u03c7":[61],"to":[64,124,301],"be":[65,91],"class":[67,81,93,161],"those":[69],"elements":[70],"that":[75,113,120,213,225,236,243,306],"have":[76],"functions":[83,97,163],"X":[84,89,158],"where":[86,262],"instance":[88],"might":[90],"\u0394":[95,126,151,219,230,259,313],"n":[96,99,127,131,141,152],"\u03c9.":[101],"x":[106,197],"we":[110,121],"will":[111,234],"say":[112],"an":[116,175,179],"X-automorphism":[117],".":[118,153,156,206],"Note":[119],"only":[122],"need":[123],"consider":[125],"-":[128],"\u03a0":[130],"-orbits":[132],"automorphisms":[134],"since":[135],"if":[136],"f":[137,144],"\u03a3":[140],"-presentation,":[142],"total":[147],"function":[148],"therefore":[150],"D":[154],"efinition":[155],"\u2286":[165],"{":[166,244,280],"i":[168,170],":":[169,246,282],"<":[171],"\u03c9},":[172],"X-orbit":[176],"iff":[177],"orbit":[180],"A,":[188],"B":[189,205,281,283,287],"there":[191,237],"satisfying":[200],"A":[202,245,247,253,265,272,277,285],"(Here":[207],"\u03a6:":[208],"\u2192":[209],".)":[210],"Harrington":[211],"proved":[212,224],"creative":[215],"form":[217,229,311],"0":[220],"-orbit":[221,315],"Soare":[223,305,317,320],"maximal":[227,307],"3":[231],"-orbit.":[232],"We":[233],"show":[235],"no":[239],"Boolean":[240],"algebra":[241],"such":[242],"\u2112":[251,263,275],"*(":[252,264,276],"\u2248":[255],"]":[256],"forms":[257],"2":[260,314],"-orbit,":[261],"principal":[269],"filter":[270],";":[274],"=":[279],"\u2286*":[284],"&":[286],"}.":[289],"The":[290],"idea":[291],"behind":[292],"proof":[294,303],"this":[296],"theorem":[297],"very":[299],"similar":[300],"by":[304],"do":[309],"not":[310],"(see":[316],"[1974]":[318],"or":[319],"[1987]).":[321]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}