{"id":"https://openalex.org/W4206256361","doi":"https://doi.org/10.1007/978-0-8176-4603-5_4","title":"Foundations of Arithmetic","display_name":"Foundations of Arithmetic","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W4206256361","doi":"https://doi.org/10.1007/978-0-8176-4603-5_4"},"language":"en","primary_location":{"id":"doi:10.1007/978-0-8176-4603-5_4","doi":"https://doi.org/10.1007/978-0-8176-4603-5_4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-0-8176-4603-5_4","pdf_url":null,"source":{"id":"https://openalex.org/S4306462921","display_name":"Birkh\u00e4user Boston eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Legacy of Mario Pieri in Geometry and Arithmetic","raw_type":"book-chapter"},"volume":{"id":"https://openalex.org/W594402137","display_name":"The Legacy of Mario Pieri in Geometry and Arithmetic"},"type":"book-chapter","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":63.5309,"has_fulltext":false,"cited_by_count":243,"citation_normalized_percentile":{"value":0.99879639,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"289","last_page":"329"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/1207","display_name":"History and Philosophy of Science"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/1207","display_name":"History and Philosophy of Science"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.0007999999797903001,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.0005000000237487257,"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/foundations-of-arithmetic","display_name":"foundations of arithmetic","score":0.9440000057220459},{"id":"https://openalex.org/keywords/consistency-of-arithmetic","display_name":"consistency of arithmetic","score":0.8309999704360962},{"id":"https://openalex.org/keywords/history-of-arithmetic","display_name":"history of arithmetic","score":0.7570000290870667}],"concepts":[{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.8052040338516235},{"id":"https://openalex.org/C112343008","wikidata":"https://www.wikidata.org/wiki/Q140744","display_name":"Arithmetic function","level":2,"score":0.7975207567214966},{"id":"https://openalex.org/C2780129039","wikidata":"https://www.wikidata.org/wiki/Q1931107","display_name":"Section (typography)","level":2,"score":0.7376217246055603},{"id":"https://openalex.org/C97489613","wikidata":"https://www.wikidata.org/wiki/Q842755","display_name":"Peano axioms","level":2,"score":0.7001739740371704},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.6621403098106384},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.5721518397331238},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5452504754066467},{"id":"https://openalex.org/C65148605","wikidata":"https://www.wikidata.org/wiki/Q7442973","display_name":"Second-order arithmetic","level":3,"score":0.504002034664154},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40224719047546387},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.38718584179878235},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2562459707260132},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2184973657131195},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2154824435710907},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09590879082679749},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"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":1,"locations":[{"id":"doi:10.1007/978-0-8176-4603-5_4","doi":"https://doi.org/10.1007/978-0-8176-4603-5_4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-0-8176-4603-5_4","pdf_url":null,"source":{"id":"https://openalex.org/S4306462921","display_name":"Birkh\u00e4user Boston eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Legacy of Mario Pieri in Geometry and Arithmetic","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7124299700","https://openalex.org/W4246958577","https://openalex.org/W3148344281","https://openalex.org/W2087202222","https://openalex.org/W2808401012","https://openalex.org/W3142312111","https://openalex.org/W2909288275","https://openalex.org/W2913639538","https://openalex.org/W2058364083","https://openalex.org/W3144319038"],"abstract_inverted_index":{"Although":[0],"primarily":[1],"a":[2],"researcher":[3],"in":[4,37,59,67,69,98,100,105,107],"geometry,":[5],"Mario":[6],"Pieri":[7],"wrote":[8],"four":[9],"papers":[10],"that":[11],"addressed":[12],"aspects":[13],"of":[14,24,33,43,46,52,73,94],"arithmetic:":[15],"1906d":[16],"A":[17],"Look":[18],"at":[19],"the":[20,25,34,41,44,50,60,70,74,83,92],"New":[21],"Logico-Mathematical":[22],"Direction":[23],"Deductive":[26],"Sciences":[27],"1906e":[28],"On":[29,40,49,91],"an":[30],"Arithmetical":[31],"Definition":[32],"Irrationals":[35],"(completed":[36],"1905)":[38],"1906g":[39],"Consistency":[42],"Axioms":[45,51,93],"Arithmetic":[47,53],"1907a":[48,87],"The":[54,89],"first":[55],"three":[56],"are":[57],"introduced":[58],"following":[61],"paragraphs,":[62],"and":[63,86,103],"will":[64],"be":[65],"discussed":[66,104],"detail":[68,106],"second":[71],"book":[72],"present":[75],"series.":[76],"Section":[77],"4.1":[78],"presents":[79],"historical":[80],"background":[81],"for":[82],"1906e,":[84],"1906g,":[85],"papers.":[88],"last,":[90],"Arithmetic,":[95],"is":[96],"translated":[97],"entirety":[99],"section":[101,108],"4.2":[102],"4.3.":[109]},"counts_by_year":[{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":22},{"year":2019,"cited_by_count":59},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":12},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":14}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2022-01-25T00:00:00"}
