{"id":"https://openalex.org/W4237105374","doi":"https://doi.org/10.1002/malq.19980440211","title":"Arithmetical Measure","display_name":"Arithmetical Measure","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W4237105374","doi":"https://doi.org/10.1002/malq.19980440211"},"language":"en","primary_location":{"id":"doi:10.1002/malq.19980440211","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19980440211","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","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/A5076144323","display_name":"Sebastiaan A. Terwijn","orcid":"https://orcid.org/0000-0002-1464-6908"},"institutions":[{"id":"https://openalex.org/I887064364","display_name":"University of Amsterdam","ror":"https://ror.org/04dkp9463","country_code":"NL","type":"education","lineage":["https://openalex.org/I887064364"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Sebastiaan A. Terwijn","raw_affiliation_strings":["Department of Mathematics and Computer Science, University of Amsterdam, Plantage Muidergracht 24, NL-1018 TV Amsterdam, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, University of Amsterdam, Plantage Muidergracht 24, NL-1018 TV Amsterdam, The Netherlands","institution_ids":["https://openalex.org/I887064364"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004254084","display_name":"Leen Torenvliet","orcid":null},"institutions":[{"id":"https://openalex.org/I887064364","display_name":"University of Amsterdam","ror":"https://ror.org/04dkp9463","country_code":"NL","type":"education","lineage":["https://openalex.org/I887064364"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Leen Torenvliet","raw_affiliation_strings":["Department of Mathematics and Computer Science, University of Amsterdam, Plantage Muidergracht 24, NL-1018 TV Amsterdam, The Netherlands","This paper is a rewritten version of a manuscript from 1995, where the comments of an anonymous referee from the JSL have been incorporated"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, University of Amsterdam, Plantage Muidergracht 24, NL-1018 TV Amsterdam, The Netherlands","institution_ids":["https://openalex.org/I887064364"]},{"raw_affiliation_string":"This paper is a rewritten version of a manuscript from 1995, where the comments of an anonymous referee from the JSL have been incorporated","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5076144323"],"corresponding_institution_ids":["https://openalex.org/I887064364"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.40643758,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"44","issue":"2","first_page":"277","last_page":"286"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":1.0,"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":1.0,"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":0.9854000210762024,"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/T13720","display_name":"Benford\u2019s Law and Fraud Detection","score":0.9800000190734863,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/measure","display_name":"Measure (data warehouse)","score":0.7844424247741699},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7784319519996643},{"id":"https://openalex.org/keywords/arithmetic-function","display_name":"Arithmetic function","score":0.681300163269043},{"id":"https://openalex.org/keywords/null-set","display_name":"Null set","score":0.6070518493652344},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6069076061248779},{"id":"https://openalex.org/keywords/turing-machine","display_name":"Turing machine","score":0.5926175713539124},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5356810688972473},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5209727883338928},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.5074905753135681},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4213813841342926},{"id":"https://openalex.org/keywords/computability-theory","display_name":"Computability theory","score":0.41519591212272644},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3907228410243988},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12936049699783325},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1004963219165802},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.05872967839241028}],"concepts":[{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.7844424247741699},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7784319519996643},{"id":"https://openalex.org/C112343008","wikidata":"https://www.wikidata.org/wiki/Q140744","display_name":"Arithmetic function","level":2,"score":0.681300163269043},{"id":"https://openalex.org/C55375708","wikidata":"https://www.wikidata.org/wiki/Q1201815","display_name":"Null set","level":3,"score":0.6070518493652344},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6069076061248779},{"id":"https://openalex.org/C29248071","wikidata":"https://www.wikidata.org/wiki/Q163310","display_name":"Turing machine","level":3,"score":0.5926175713539124},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5356810688972473},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5209727883338928},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.5074905753135681},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4213813841342926},{"id":"https://openalex.org/C111142201","wikidata":"https://www.wikidata.org/wiki/Q818930","display_name":"Computability theory","level":2,"score":0.41519591212272644},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3907228410243988},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12936049699783325},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1004963219165802},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05872967839241028},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","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/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1002/malq.19980440211","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19980440211","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.143.6923","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.143.6923","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://staff.science.uva.nl/~terwijn/publications/me.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.143.9642","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.143.9642","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://staff.science.uva.nl/~terwijn/publications/me.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.8.84","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.8.84","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://turing.wins.uva.nl/%7Eleen/PAPERS/me.ps.gz","raw_type":"text"},{"id":"pmh:oai:dare.uva.nl:openaire_cris_publications/e66f4ff2-f4a4-4a34-8706-86dbf94bbe17","is_oa":false,"landing_page_url":"https://handle.uba.uva.nl/personal/pure/en/publications/arithmetical-measure(e66f4ff2-f4a4-4a34-8706-86dbf94bbe17).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Terwijn, S & Torenvliet, L 1998, 'Arithmetical Measure', Mathematical Logic Quarterly, vol. 44, pp. 277-286. https://doi.org/10.1002/malq.19980440211","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:dare.uva.nl:publications/e66f4ff2-f4a4-4a34-8706-86dbf94bbe17","is_oa":false,"landing_page_url":"http://dare.uva.nl/personal/pure/en/publications/arithmetical-measure(e66f4ff2-f4a4-4a34-8706-86dbf94bbe17).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Terwijn, S & Torenvliet, L 1998, 'Arithmetical Measure', Mathematical Logic Quarterly, vol. 44, pp. 277-286. https://doi.org/10.1002/malq.19980440211","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:uvapub:oai:dare.uva.nl:publications/e66f4ff2-f4a4-4a34-8706-86dbf94bbe17","is_oa":false,"landing_page_url":"https://dare.uva.nl/personal/pure/en/publications/arithmetical-measure(e66f4ff2-f4a4-4a34-8706-86dbf94bbe17).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematical Logic Quarterly, 44, 277 - 286. Wiley-VCH Verlag","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W10794601","https://openalex.org/W1972067040","https://openalex.org/W2059835508","https://openalex.org/W2067580807","https://openalex.org/W2169825513","https://openalex.org/W2176419554","https://openalex.org/W2316459924","https://openalex.org/W2499081645","https://openalex.org/W2574999163","https://openalex.org/W2939498485","https://openalex.org/W3003623942","https://openalex.org/W4232277851"],"related_works":["https://openalex.org/W4388310202","https://openalex.org/W2310420552","https://openalex.org/W2133902039","https://openalex.org/W1589207578","https://openalex.org/W2936847277","https://openalex.org/W167110062","https://openalex.org/W4597164","https://openalex.org/W1161578261","https://openalex.org/W90338445","https://openalex.org/W4232694312"],"abstract_inverted_index":{"Abstract":[0],"We":[1,29,80],"develop":[2],"arithmetical":[3],"measure":[4,18,112,115],"theory":[5],"along":[6],"the":[7,14,32,43,59,73,83,109],"lines":[8],"of":[9,17,34,42,61,72,85,158],"Lutz":[10,45],"[10].":[11],"This":[12],"yields":[13],"same":[15],"notion":[16],"0":[19],"set":[20,136,147],"as":[21],"considered":[22],"before":[23],"by":[24,37,155],"Martin\u2010L\u00f6f,":[25],"Schnorr,":[26],"and":[27,64,96,114,122,143],"others.":[28],"prove":[30],"that":[31,82,87,98,130,137,144],"class":[33,60,68,84],"sets":[35,86],"constructible":[36],"r.e.\u2010constructors,":[38],"a":[39,133,156,160],"direct":[40],"analogue":[41],"classes":[44],"devised":[46],"his":[47],"resource":[48],"bounded":[49,88],"measures":[50],"for":[51],"in":[52,70],"[10],":[53],"is":[54,138,148],"not":[55],"equal":[56],"to":[57,91,103,125,140,150],"RE,":[58],"r.e.":[62],"sets,":[63],"we":[65],"locate":[66],"this":[67,99],"exactly":[69],"terms":[71],"common":[74],"recursion\u2010theoretic":[75],"reducibilities":[76],"below":[77],"K":[78,92,126,141,151],".":[79,127,152],"note":[81],"truth\u2010table":[89,120],"reduce":[90],"has":[93],"r.e.\u2010measure":[94],"0,":[95],"show":[97],"cannot":[100],"be":[101],"improved":[102],"truth\u2010table.":[104],"For":[105],"\u0394":[106],"2":[107],"\u2010measure":[108],"borderline":[110],"between":[111,118],"zero":[113],"nonzero":[116],"lies":[117],"weak":[119],"reducibility":[121,124],"Turing":[123],"It":[128],"follows":[129],"there":[131],"exists":[132],"Martin\u2010L\u00f6f":[134],"random":[135],"tt\u2010reducible":[139],",":[142],"no":[145],"such":[146],"btt\u2010reducible":[149],"In":[153],"fact,":[154],"result":[157,164],"Kautz,":[159],"much":[161],"more":[162],"general":[163],"holds.":[165]},"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
