{"id":"https://openalex.org/W2324792240","doi":"https://doi.org/10.1215/00294527-3489987","title":"Some Remarks on Real Numbers Induced by First-Order Spectra","display_name":"Some Remarks on Real Numbers Induced by First-Order Spectra","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2324792240","doi":"https://doi.org/10.1215/00294527-3489987","mag":"2324792240"},"language":"en","primary_location":{"id":"doi:10.1215/00294527-3489987","is_oa":false,"landing_page_url":"https://doi.org/10.1215/00294527-3489987","pdf_url":null,"source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal 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/A5105250194","display_name":"Sune Kristian Jakobsen","orcid":null},"institutions":[{"id":"https://openalex.org/I124055696","display_name":"University of Copenhagen","ror":"https://ror.org/035b05819","country_code":"DK","type":"education","lineage":["https://openalex.org/I124055696"]}],"countries":["DK"],"is_corresponding":true,"raw_author_name":"Sune Kristian Jakobsen","raw_affiliation_strings":["Department of Mathematical Sciences University of Copenhagen Universitetsparken 5 DK-2100 Copenhagen \u00d8 Denmark","Department of Computer Science University of Copenhagen (DIKU) Njalsgade 128-132 DK-2300 Copenhagen S Denmark"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences University of Copenhagen Universitetsparken 5 DK-2100 Copenhagen \u00d8 Denmark","institution_ids":["https://openalex.org/I124055696"]},{"raw_affiliation_string":"Department of Computer Science University of Copenhagen (DIKU) Njalsgade 128-132 DK-2300 Copenhagen S Denmark","institution_ids":["https://openalex.org/I124055696"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024664299","display_name":"Jakob Grue Simonsen","orcid":"https://orcid.org/0000-0002-3488-9392"},"institutions":[{"id":"https://openalex.org/I124055696","display_name":"University of Copenhagen","ror":"https://ror.org/035b05819","country_code":"DK","type":"education","lineage":["https://openalex.org/I124055696"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Jakob Grue Simonsen","raw_affiliation_strings":["Department of Mathematical Sciences University of Copenhagen Universitetsparken 5 DK-2100 Copenhagen \u00d8 Denmark","Department of Computer Science University of Copenhagen (DIKU) Njalsgade 128-132 DK-2300 Copenhagen S Denmark"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences University of Copenhagen Universitetsparken 5 DK-2100 Copenhagen \u00d8 Denmark","institution_ids":["https://openalex.org/I124055696"]},{"raw_affiliation_string":"Department of Computer Science University of Copenhagen (DIKU) Njalsgade 128-132 DK-2300 Copenhagen S Denmark","institution_ids":["https://openalex.org/I124055696"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5105250194"],"corresponding_institution_ids":["https://openalex.org/I124055696"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.03254517,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"57","issue":"3","first_page":null,"last_page":null},"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":0.9966999888420105,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9958999752998352,"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/real-number","display_name":"Real number","score":0.7081993818283081},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6143320798873901},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5737618803977966},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.54671311378479},{"id":"https://openalex.org/keywords/spectrum","display_name":"Spectrum (functional analysis)","score":0.5086796879768372},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.499326229095459},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.46991196274757385},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46479886770248413},{"id":"https://openalex.org/keywords/topological-entropy","display_name":"Topological entropy","score":0.4507262706756592},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4151357114315033},{"id":"https://openalex.org/keywords/open-set","display_name":"Open set","score":0.41054069995880127},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37695837020874023},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2241552770137787},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11397296190261841},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08323001861572266},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06405532360076904}],"concepts":[{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.7081993818283081},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6143320798873901},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5737618803977966},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.54671311378479},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.5086796879768372},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.499326229095459},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.46991196274757385},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46479886770248413},{"id":"https://openalex.org/C2780350623","wikidata":"https://www.wikidata.org/wiki/Q3055355","display_name":"Topological entropy","level":2,"score":0.4507262706756592},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4151357114315033},{"id":"https://openalex.org/C42357961","wikidata":"https://www.wikidata.org/wiki/Q213363","display_name":"Open set","level":2,"score":0.41054069995880127},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37695837020874023},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2241552770137787},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11397296190261841},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08323001861572266},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06405532360076904},{"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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1215/00294527-3489987","is_oa":false,"landing_page_url":"https://doi.org/10.1215/00294527-3489987","pdf_url":null,"source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.ndjfl/1458829375","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1458829375","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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/677e400d-b0ec-44c7-92cd-1611626879ac","is_oa":false,"landing_page_url":"https://researchprofiles.ku.dk/da/publications/677e400d-b0ec-44c7-92cd-1611626879ac","pdf_url":null,"source":{"id":"https://openalex.org/S4306401983","display_name":"Research at the University of Copenhagen (University of Copenhagen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I124055696","host_organization_name":"University of Copenhagen","host_organization_lineage":["https://openalex.org/I124055696"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Jakobsen , S & Simonsen , J G 2016 , ' Some remarks on real numbers induced by first-order spectra ' , Notre Dame Journal of Formal Logic , vol. 57 , no. 3 , pp. 355-368 . https://doi.org/10.1215/00294527-3489987","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.41999998688697815,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W954689","https://openalex.org/W1489341787","https://openalex.org/W1509579779","https://openalex.org/W1545819195","https://openalex.org/W1565611252","https://openalex.org/W1981198727","https://openalex.org/W1994584977","https://openalex.org/W2006876805","https://openalex.org/W2017473312","https://openalex.org/W2018446984","https://openalex.org/W2022731279","https://openalex.org/W2046937767","https://openalex.org/W2051452796","https://openalex.org/W2065706312","https://openalex.org/W2076597612","https://openalex.org/W2082778556","https://openalex.org/W2125495920","https://openalex.org/W2126160338","https://openalex.org/W2171462076","https://openalex.org/W2950455125","https://openalex.org/W4206252072","https://openalex.org/W4237721941","https://openalex.org/W4238159413","https://openalex.org/W4253795631","https://openalex.org/W4301330952"],"related_works":["https://openalex.org/W1490569688","https://openalex.org/W2626419576","https://openalex.org/W2955814494","https://openalex.org/W2527877093","https://openalex.org/W2910576907","https://openalex.org/W4381747479","https://openalex.org/W2594052908","https://openalex.org/W2952193096","https://openalex.org/W4404989081","https://openalex.org/W142164690"],"abstract_inverted_index":{"The":[0],"spectrum":[1],"of":[2,9,16,19,33,71,94,122,135,154],"a":[3,23,30,95,123],"first-order":[4],"sentence":[5],"is":[6,82,88,98,138,157],"the":[7,14,20,36,52,72,91,119,133,152],"set":[8,134],"natural":[10],"numbers":[11],"occurring":[12],"as":[13,60,62,118],"cardinalities":[15],"finite":[17],"models":[18],"sentence.":[21],"In":[22,51,126],"recent":[24],"survey,":[25],"Durand":[26,128],"et":[27,129],"al.":[28,130],"introduce":[29],"new":[31],"class":[32,153],"real":[34,81,87,97,111],"numbers,":[35],"spectral":[37,96,124,136,155],"reals,":[38],"induced":[39],"by":[40,149],"spectra":[41],"and":[42,103,107,115],"pose":[43],"two":[44],"open":[45,58,64],"problems":[46,59,65],"associated":[47],"to":[48],"this":[49,147],"class.":[50],"present":[53],"note,":[54],"we":[55,75],"answer":[56],"these":[57],"well":[61],"other":[63],"from":[66],"an":[67],"earlier,":[68],"unpublished":[69],"version":[70],"survey.":[73],"Specifically,":[74],"prove":[76],"that":[77,132,151],"(i)":[78],"every":[79,85,109],"algebraic":[80],"spectral,":[83,89],"(ii)":[84],"automatic":[86],"(iii)":[90],"subword":[92,120],"density":[93],"either":[99],"0":[100,114],"or":[101,143],"1,":[102],"both":[104],"may":[105],"occur,":[106],"(iv)":[108],"right-computable":[110],"number":[112],"between":[113],"1":[116],"occurs":[117],"entropy":[121],"real.":[125],"addition,":[127],"note":[131],"reals":[137,156],"not":[139,158],"closed":[140,159],"under":[141,160],"addition":[142],"multiplication.":[144],"We":[145],"extend":[146],"result":[148],"showing":[150],"any":[161],"computable":[162],"operation":[163],"satisfying":[164],"some":[165],"mild":[166],"conditions.":[167]},"counts_by_year":[],"updated_date":"2026-03-17T09:09:15.849793","created_date":"2025-10-10T00:00:00"}
