{"id":"https://openalex.org/W2088914813","doi":"https://doi.org/10.1007/s00153-007-0059-x","title":"The elementary computable functions over the real numbers: applying two new techniques","display_name":"The elementary computable functions over the real numbers: applying two new techniques","publication_year":2007,"publication_date":"2007-11-26","ids":{"openalex":"https://openalex.org/W2088914813","doi":"https://doi.org/10.1007/s00153-007-0059-x","mag":"2088914813"},"language":"en","primary_location":{"id":"doi:10.1007/s00153-007-0059-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00153-007-0059-x","pdf_url":null,"source":{"id":"https://openalex.org/S188076996","display_name":"Archive for Mathematical Logic","issn_l":"0933-5846","issn":["0933-5846","1432-0665"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Archive for Mathematical 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/A5021432473","display_name":"Manuel L. Campagnolo","orcid":"https://orcid.org/0000-0002-9634-3061"},"institutions":[{"id":"https://openalex.org/I4210120471","display_name":"Instituto de Telecomunica\u00e7\u00f5es","ror":"https://ror.org/02ht4fk33","country_code":"PT","type":"nonprofit","lineage":["https://openalex.org/I4210120471"]}],"countries":["PT"],"is_corresponding":true,"raw_author_name":"Manuel L. Campagnolo","raw_affiliation_strings":["Departamento de Matem\u00e1tica, Instituto Superior de Agronomia, Lisbon University of Technology, Tapada da Ajuda, 1349-017, Lisbon, Portugal","SQIG/Instituto de Telecomunica\u00e7\u00f5es, Lisbon, Portugal"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica, Instituto Superior de Agronomia, Lisbon University of Technology, Tapada da Ajuda, 1349-017, Lisbon, Portugal","institution_ids":[]},{"raw_affiliation_string":"SQIG/Instituto de Telecomunica\u00e7\u00f5es, Lisbon, Portugal","institution_ids":["https://openalex.org/I4210120471"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081962331","display_name":"Kerry Ojakian","orcid":null},"institutions":[{"id":"https://openalex.org/I4210120471","display_name":"Instituto de Telecomunica\u00e7\u00f5es","ror":"https://ror.org/02ht4fk33","country_code":"PT","type":"nonprofit","lineage":["https://openalex.org/I4210120471"]},{"id":"https://openalex.org/I4387152517","display_name":"Instituto Superior T\u00e9cnico","ror":"https://ror.org/03db2by73","country_code":null,"type":"education","lineage":["https://openalex.org/I141596103","https://openalex.org/I4387152517"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Kerry Ojakian","raw_affiliation_strings":["Departamento de Matem\u00e1tica, Instituto Superior T\u00e9cnico, Av. Rovisco Pais, 1049-001, Lisbon, Portugal","SQIG/Instituto de Telecomunica\u00e7\u00f5es, Lisbon, Portugal"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica, Instituto Superior T\u00e9cnico, Av. Rovisco Pais, 1049-001, Lisbon, Portugal","institution_ids":["https://openalex.org/I4387152517"]},{"raw_affiliation_string":"SQIG/Instituto de Telecomunica\u00e7\u00f5es, Lisbon, Portugal","institution_ids":["https://openalex.org/I4210120471"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5021432473"],"corresponding_institution_ids":["https://openalex.org/I4210120471"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":2.9886,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.90963058,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"46","issue":"7-8","first_page":"593","last_page":"627"},"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/T13720","display_name":"Benford\u2019s Law and Fraud Detection","score":0.9811000227928162,"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"}},{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9611999988555908,"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":0.7385180592536926},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.6310679912567139},{"id":"https://openalex.org/keywords/elementary-function","display_name":"Elementary function","score":0.5469167828559875},{"id":"https://openalex.org/keywords/computable-analysis","display_name":"Computable analysis","score":0.5053065419197083},{"id":"https://openalex.org/keywords/computable-function","display_name":"Computable function","score":0.48294371366500854},{"id":"https://openalex.org/keywords/computable-number","display_name":"Computable number","score":0.4663523733615875},{"id":"https://openalex.org/keywords/mathematics-education","display_name":"Mathematics education","score":0.45549285411834717},{"id":"https://openalex.org/keywords/mathematical-logic","display_name":"Mathematical logic","score":0.41215741634368896},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.36728382110595703},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3358939588069916},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3200058341026306},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2773835361003876},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.14223676919937134},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.05783224105834961}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7385180592536926},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.6310679912567139},{"id":"https://openalex.org/C182408441","wikidata":"https://www.wikidata.org/wiki/Q824282","display_name":"Elementary function","level":2,"score":0.5469167828559875},{"id":"https://openalex.org/C27318111","wikidata":"https://www.wikidata.org/wiki/Q5157264","display_name":"Computable analysis","level":3,"score":0.5053065419197083},{"id":"https://openalex.org/C54271186","wikidata":"https://www.wikidata.org/wiki/Q1148456","display_name":"Computable function","level":2,"score":0.48294371366500854},{"id":"https://openalex.org/C156382255","wikidata":"https://www.wikidata.org/wiki/Q818895","display_name":"Computable number","level":4,"score":0.4663523733615875},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.45549285411834717},{"id":"https://openalex.org/C47884741","wikidata":"https://www.wikidata.org/wiki/Q1166618","display_name":"Mathematical logic","level":2,"score":0.41215741634368896},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.36728382110595703},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3358939588069916},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3200058341026306},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2773835361003876},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14223676919937134},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05783224105834961},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00153-007-0059-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00153-007-0059-x","pdf_url":null,"source":{"id":"https://openalex.org/S188076996","display_name":"Archive for Mathematical Logic","issn_l":"0933-5846","issn":["0933-5846","1432-0665"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Archive for Mathematical Logic","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.64.1626","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.64.1626","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://wslc.math.ist.utl.pt/ftp/pub/CampagnoloM/07-CO-elem.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W177079861","https://openalex.org/W745134671","https://openalex.org/W1509579779","https://openalex.org/W1545819195","https://openalex.org/W1882278886","https://openalex.org/W1965850345","https://openalex.org/W1985213782","https://openalex.org/W1985531779","https://openalex.org/W1992205856","https://openalex.org/W2050204928","https://openalex.org/W2108904240","https://openalex.org/W2116509046","https://openalex.org/W2120926795","https://openalex.org/W2168711698","https://openalex.org/W4239497877","https://openalex.org/W4243563333"],"related_works":["https://openalex.org/W197714092","https://openalex.org/W2150482238","https://openalex.org/W1577501449","https://openalex.org/W153068418","https://openalex.org/W2527631632","https://openalex.org/W1994403863","https://openalex.org/W2108904240","https://openalex.org/W1987175852","https://openalex.org/W1498085647","https://openalex.org/W2080359559"],"abstract_inverted_index":null,"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}