{"id":"https://openalex.org/W1516895917","doi":"https://doi.org/10.37236/1452","title":"Reconstructing Subsets of Reals","display_name":"Reconstructing Subsets of Reals","publication_year":1999,"publication_date":"1999-03-15","ids":{"openalex":"https://openalex.org/W1516895917","doi":"https://doi.org/10.37236/1452","mag":"1516895917"},"language":"en","primary_location":{"id":"doi:10.37236/1452","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1452","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v6i1r20/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v6i1r20/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032520716","display_name":"A. J. Radcliffe","orcid":"https://orcid.org/0000-0002-8817-0383"},"institutions":[{"id":"https://openalex.org/I114395901","display_name":"University of Nebraska\u2013Lincoln","ror":"https://ror.org/043mer456","country_code":"US","type":"education","lineage":["https://openalex.org/I114395901"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. J. Radcliffe","raw_affiliation_strings":["#N##TAB##TAB##TAB##TAB# University of Nebraska-Lincoln#N##TAB##TAB##TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"#N##TAB##TAB##TAB##TAB# University of Nebraska-Lincoln#N##TAB##TAB##TAB#","institution_ids":["https://openalex.org/I114395901"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045091550","display_name":"Alex Scott","orcid":"https://orcid.org/0000-0003-4489-5988"},"institutions":[{"id":"https://openalex.org/I114395901","display_name":"University of Nebraska\u2013Lincoln","ror":"https://ror.org/043mer456","country_code":"US","type":"education","lineage":["https://openalex.org/I114395901"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. D. Scott","raw_affiliation_strings":["Department of Mathematics University College Gower Street London WC1E 6BT","Department of Mathematics and Statistics","University of Nebraska-Lincoln Lincoln, NE 68588-0323"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics University College Gower Street London WC1E 6BT","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics and Statistics","institution_ids":[]},{"raw_affiliation_string":"University of Nebraska-Lincoln Lincoln, NE 68588-0323","institution_ids":["https://openalex.org/I114395901"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I114395901"],"apc_list":null,"apc_paid":null,"fwci":1.8461,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.8144885,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"6","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9937000274658203,"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":0.9937000274658203,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9865000247955322,"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":0.9847999811172485,"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/multiset","display_name":"Multiset","score":0.9882621765136719},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8610067367553711},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6929786801338196},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.6880301237106323},{"id":"https://openalex.org/keywords/translation","display_name":"Translation (biology)","score":0.6487056612968445},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5322456359863281},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5134502649307251},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08007708191871643}],"concepts":[{"id":"https://openalex.org/C2779623528","wikidata":"https://www.wikidata.org/wiki/Q864377","display_name":"Multiset","level":2,"score":0.9882621765136719},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8610067367553711},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6929786801338196},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.6880301237106323},{"id":"https://openalex.org/C149364088","wikidata":"https://www.wikidata.org/wiki/Q185917","display_name":"Translation (biology)","level":4,"score":0.6487056612968445},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5322456359863281},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5134502649307251},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08007708191871643},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C105580179","wikidata":"https://www.wikidata.org/wiki/Q188928","display_name":"Messenger RNA","level":3,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.37236/1452","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1452","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v6i1r20/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:digitalcommons.unl.edu:mathfacpub-1141","is_oa":false,"landing_page_url":"https://digitalcommons.unl.edu/mathfacpub/145","pdf_url":null,"source":{"id":"https://openalex.org/S4306400577","display_name":"Lincoln (University of Nebraska)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I114395901","host_organization_name":"University of Nebraska\u2013Lincoln","host_organization_lineage":["https://openalex.org/I114395901"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Department of Mathematics: Faculty Publications","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.176.3111","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.176.3111","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://people.maths.ox.ac.uk/%7Escott/Papers/zqr.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.44.2499","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.44.2499","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mat.ub.es/EMIS/journals/EJC/Volume_6/PostScriptfiles/v6i1r20.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.46.5316","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.46.5316","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emis.de/journals/EJC/Volume_6/PDF/v6i1r20.pdf","raw_type":"text"},{"id":"pmh:oai:eprints.ucl.ac.uk.OAI2:188613","is_oa":false,"landing_page_url":"http://discovery.ucl.ac.uk/188613/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400024","display_name":"UCL Discovery (University College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45129253","host_organization_name":"University College London","host_organization_lineage":["https://openalex.org/I45129253"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Electronic Journal of Combinatorics , 6 Research-. (1999)","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.37236/1452","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1452","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v6i1r20/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6657950","display_name":"Sauer Problems for Set Systems","funder_award_id":"9401351","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1516895917.pdf","grobid_xml":"https://content.openalex.org/works/W1516895917.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W67379874","https://openalex.org/W170887361","https://openalex.org/W1985188710","https://openalex.org/W2029726795","https://openalex.org/W2058068142","https://openalex.org/W2075084424","https://openalex.org/W2989634522"],"related_works":["https://openalex.org/W4300455649","https://openalex.org/W2296588302","https://openalex.org/W4328119206","https://openalex.org/W2033245919","https://openalex.org/W4252409532","https://openalex.org/W2006067547","https://openalex.org/W1516895917","https://openalex.org/W1977456141","https://openalex.org/W4387031542","https://openalex.org/W2142539551"],"abstract_inverted_index":{"We":[0,49,79],"consider":[1],"the":[2,15,91],"problem":[3],"of":[4,8,17,20,37,43,47,56,69,74,86,93],"reconstructing":[5],"a":[6],"set":[7,73],"real":[9],"numbers":[10],"up":[11,24,97],"to":[12,25,54,98],"translation":[13],"from":[14,90],"multiset":[16,92],"its":[18,94],"subsets":[19,36,55],"fixed":[21],"size,":[22],"given":[23,71,96],"translation.":[26,99],"This":[27],"is":[28,88],"impossible":[29],"in":[30],"general:":[31],"for":[32],"instance":[33],"almost":[34],"all":[35],"$\\mathbb{Z}$":[38],"contain":[39,64],"infinitely":[40],"many":[41,67],"translates":[42,68],"every":[44,82],"finite":[45,72,84],"subset":[46,85],"$\\mathbb{Z}$.":[48],"therefore":[50],"restrict":[51],"our":[52],"attention":[53],"$\\mathbb{R}$":[57,87],"which":[58,63],"are":[59],"locally":[60,83],"finite;":[61],"those":[62],"only":[65],"finitely":[66],"any":[70],"size":[75],"at":[76],"least":[77],"2.":[78],"prove":[80],"that":[81],"reconstructible":[89],"3-subsets,":[95]},"counts_by_year":[],"updated_date":"2026-07-27T08:26:11.824852","created_date":"2025-10-10T00:00:00"}
