{"id":"https://openalex.org/W1978053327","doi":"https://doi.org/10.1007/s00153-008-0102-6","title":"Fruitful and helpful ordinal functions","display_name":"Fruitful and helpful ordinal functions","publication_year":2008,"publication_date":"2008-09-24","ids":{"openalex":"https://openalex.org/W1978053327","doi":"https://doi.org/10.1007/s00153-008-0102-6","mag":"1978053327"},"language":"en","primary_location":{"id":"doi:10.1007/s00153-008-0102-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00153-008-0102-6","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/A5049756356","display_name":"Harold Simmons","orcid":null},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Harold Simmons","raw_affiliation_strings":["School of Mathematics, The University, Manchester, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, The University, Manchester, UK","institution_ids":["https://openalex.org/I28407311"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5049756356"],"corresponding_institution_ids":["https://openalex.org/I28407311"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.07018679,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"47","issue":"7-8","first_page":"677","last_page":"709"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.24070000648498535,"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":0.24070000648498535,"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/T10126","display_name":"Logic, programming, and type systems","score":0.23960000276565552,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11727","display_name":"Advanced Algebra and Logic","score":0.11800000071525574,"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":0.7547010779380798},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.613784670829773},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6012853980064392},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.5929918885231018},{"id":"https://openalex.org/keywords/uncountable-set","display_name":"Uncountable set","score":0.5076538324356079},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.4538399875164032},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4493187665939331},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.43917977809906006},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4196828007698059},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3352373540401459},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.20194613933563232},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19208744168281555},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15486815571784973},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0686633288860321}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7547010779380798},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.613784670829773},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6012853980064392},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.5929918885231018},{"id":"https://openalex.org/C142399903","wikidata":"https://www.wikidata.org/wiki/Q1128796","display_name":"Uncountable set","level":3,"score":0.5076538324356079},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.4538399875164032},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4493187665939331},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.43917977809906006},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4196828007698059},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3352373540401459},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.20194613933563232},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19208744168281555},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15486815571784973},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0686633288860321},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00153-008-0102-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00153-008-0102-6","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:10.1.1.367.5375","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.367.5375","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.man.ac.uk/~hsimmons/ORDINAL-NOTATIONS/Fruitful.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":6,"referenced_works":["https://openalex.org/W327533636","https://openalex.org/W2007823114","https://openalex.org/W2014501253","https://openalex.org/W2056098697","https://openalex.org/W2314560038","https://openalex.org/W2475785644"],"related_works":["https://openalex.org/W3019662020","https://openalex.org/W4297571715","https://openalex.org/W2100222222","https://openalex.org/W2512721618","https://openalex.org/W2600675026","https://openalex.org/W3139954723","https://openalex.org/W4242301765","https://openalex.org/W1519257018","https://openalex.org/W3097468110","https://openalex.org/W2328843190"],"abstract_inverted_index":null,"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
