{"id":"https://openalex.org/W2035802665","doi":"https://doi.org/10.1002/1521-3870(200108)47:3<423::aid-malq423>3.0.co;2-0","title":"Non-constructive Properties of the Real Numbers","display_name":"Non-constructive Properties of the Real Numbers","publication_year":2001,"publication_date":"2001-08-01","ids":{"openalex":"https://openalex.org/W2035802665","doi":"https://doi.org/10.1002/1521-3870(200108)47:3<423::aid-malq423>3.0.co;2-0","mag":"2035802665"},"language":"en","primary_location":{"id":"doi:10.1002/1521-3870(200108)47:3<423::aid-malq423>3.0.co;2-0","is_oa":false,"landing_page_url":"https://doi.org/10.1002/1521-3870(200108)47:3<423::aid-malq423>3.0.co;2-0","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":"MLQ","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/A5025418958","display_name":"Paul Howard","orcid":"https://orcid.org/0000-0001-8649-0511"},"institutions":[{"id":"https://openalex.org/I138216421","display_name":"Eastern Michigan University","ror":"https://ror.org/02ehshm78","country_code":"US","type":"education","lineage":["https://openalex.org/I138216421"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Paul Howard","raw_affiliation_strings":["Department of Mathematics, Eastern Michigan University, Ypsilanti, MI 48197, U.S.A","Department of Mathematics, Eastern Michigan University, Ypsilanti, MI 48197, U, S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Eastern Michigan University, Ypsilanti, MI 48197, U.S.A","institution_ids":["https://openalex.org/I138216421"]},{"raw_affiliation_string":"Department of Mathematics, Eastern Michigan University, Ypsilanti, MI 48197, U, S.A","institution_ids":["https://openalex.org/I138216421"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028285276","display_name":"Kyriakos Keremedis","orcid":"https://orcid.org/0000-0001-8453-3477"},"institutions":[{"id":"https://openalex.org/I98805295","display_name":"University of the Aegean","ror":"https://ror.org/03zsp3p94","country_code":"GR","type":"education","lineage":["https://openalex.org/I98805295"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Kyriakos Keremedis","raw_affiliation_strings":["Department of Mathematics, University of the Aegean, Karlovasi, Samos 83200, Greece","Department of Mathematics, University of the Aegean Karlovasi, Samos, 83200, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of the Aegean, Karlovasi, Samos 83200, Greece","institution_ids":["https://openalex.org/I98805295"]},{"raw_affiliation_string":"Department of Mathematics, University of the Aegean Karlovasi, Samos, 83200, Greece","institution_ids":["https://openalex.org/I98805295"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073538536","display_name":"Jean E. Rubin","orcid":null},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jean E. Rubin","raw_affiliation_strings":["Department of Mathematics, Purdue University, West Lafayette, IN 47907, U.S.A","Department of Mathematics , Purdue University West Lafayette , IN, 47907, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Purdue University, West Lafayette, IN 47907, U.S.A","institution_ids":["https://openalex.org/I219193219"]},{"raw_affiliation_string":"Department of Mathematics , Purdue University West Lafayette , IN, 47907, U.S.A","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018152831","display_name":"Adrienne Stanley","orcid":"https://orcid.org/0009-0005-3110-1335"},"institutions":[{"id":"https://openalex.org/I119234918","display_name":"University of Northern Iowa","ror":"https://ror.org/02h4qpx12","country_code":"US","type":"education","lineage":["https://openalex.org/I119234918"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Adrienne Stanley","raw_affiliation_strings":["Department of Mathematics, University of Northern Iowa, Cedar Falls, IA 50614, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Northern Iowa, Cedar Falls, IA 50614, U.S.A","institution_ids":["https://openalex.org/I119234918"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088225793","display_name":"Eleftherios Tatchtsis","orcid":null},"institutions":[{"id":"https://openalex.org/I98805295","display_name":"University of the Aegean","ror":"https://ror.org/03zsp3p94","country_code":"GR","type":"education","lineage":["https://openalex.org/I98805295"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Eleftherios Tatchtsis","raw_affiliation_strings":["Department of Mathematics, University of the Aegean, Karlovasi, Samos 83200, Greece","Department of Mathematics, University of the Aegean Karlovasi, Samos, 83200, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of the Aegean, Karlovasi, Samos 83200, Greece","institution_ids":["https://openalex.org/I98805295"]},{"raw_affiliation_string":"Department of Mathematics, University of the Aegean Karlovasi, Samos, 83200, Greece","institution_ids":["https://openalex.org/I98805295"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":3.3782,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.92172083,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"47","issue":"3","first_page":"423","last_page":"431"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9990000128746033,"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":0.9990000128746033,"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":0.9990000128746033,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.992900013923645,"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/mathematics","display_name":"Mathematics","score":0.8626673221588135},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.6468896865844727},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3340528905391693},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08150458335876465},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.05031043291091919}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8626673221588135},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.6468896865844727},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3340528905391693},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08150458335876465},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.05031043291091919},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1002/1521-3870(200108)47:3<423::aid-malq423>3.0.co;2-0","is_oa":false,"landing_page_url":"https://doi.org/10.1002/1521-3870(200108)47:3<423::aid-malq423>3.0.co;2-0","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":"MLQ","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.85.1438","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.85.1438","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.purdue.edu/~jer/Papers/non-constructive.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.4399999976158142,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1132673866","https://openalex.org/W1541012876","https://openalex.org/W1608084331","https://openalex.org/W1978413491","https://openalex.org/W2030402678","https://openalex.org/W2115456387"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W4230623537","https://openalex.org/W2063488590","https://openalex.org/W2232548288","https://openalex.org/W1624588321","https://openalex.org/W182461575"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,8],"relationship":[3],"between":[4],"various":[5],"properties":[6],"of":[7],"real":[9],"numbers":[10],"and":[11],"weak":[12],"choice":[13],"principles.":[14]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}