{"id":"https://openalex.org/W2171341762","doi":"https://doi.org/10.1093/jigpal/jzm013","title":"An Introduction to Basic Arithmetic","display_name":"An Introduction to Basic Arithmetic","publication_year":2007,"publication_date":"2007-07-10","ids":{"openalex":"https://openalex.org/W2171341762","doi":"https://doi.org/10.1093/jigpal/jzm013","mag":"2171341762"},"language":"en","primary_location":{"id":"doi:10.1093/jigpal/jzm013","is_oa":false,"landing_page_url":"https://doi.org/10.1093/jigpal/jzm013","pdf_url":null,"source":{"id":"https://openalex.org/S2734381524","display_name":"Logic Journal of IGPL","issn_l":"1367-0751","issn":["1367-0751","1368-9894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logic Journal of IGPL","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/A5030545131","display_name":"Mohammad Ardeshir","orcid":null},"institutions":[{"id":"https://openalex.org/I133529467","display_name":"Sharif University of Technology","ror":"https://ror.org/024c2fq17","country_code":"IR","type":"education","lineage":["https://openalex.org/I133529467"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"M. Ardeshir","raw_affiliation_strings":["Department of Mathematics, Sharif University of Technology, P.O. Box\r\n                11365-9415, Tehran, Iran. E-mail: mardeshir@sharif.edu"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sharif University of Technology, P.O. Box\r\n                11365-9415, Tehran, Iran. E-mail: mardeshir@sharif.edu","institution_ids":["https://openalex.org/I133529467"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070863416","display_name":"Bardyaa Hesaam","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"B. Hesaam","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5030545131"],"corresponding_institution_ids":["https://openalex.org/I133529467"],"apc_list":{"value":4151,"currency":"USD","value_usd":4151},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.12974439,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"16","issue":"1","first_page":"1","last_page":"13"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9994999766349792,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9983999729156494,"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/T10142","display_name":"Formal Methods in Verification","score":0.9970999956130981,"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/arithmetic","display_name":"Arithmetic","score":0.6236363053321838},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.5970080494880676},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5811647176742554},{"id":"https://openalex.org/keywords/peano-axioms","display_name":"Peano axioms","score":0.5146928429603577},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5143383741378784},{"id":"https://openalex.org/keywords/fragment","display_name":"Fragment (logic)","score":0.4348650872707367},{"id":"https://openalex.org/keywords/schema","display_name":"Schema (genetic algorithms)","score":0.4333561062812805},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4069913327693939},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3983980119228363},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.37195900082588196},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22259002923965454},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1740480661392212},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.13287290930747986}],"concepts":[{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.6236363053321838},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5970080494880676},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5811647176742554},{"id":"https://openalex.org/C97489613","wikidata":"https://www.wikidata.org/wiki/Q842755","display_name":"Peano axioms","level":2,"score":0.5146928429603577},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5143383741378784},{"id":"https://openalex.org/C2776235265","wikidata":"https://www.wikidata.org/wiki/Q18392052","display_name":"Fragment (logic)","level":2,"score":0.4348650872707367},{"id":"https://openalex.org/C52146309","wikidata":"https://www.wikidata.org/wiki/Q7431116","display_name":"Schema (genetic algorithms)","level":2,"score":0.4333561062812805},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4069913327693939},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3983980119228363},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.37195900082588196},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22259002923965454},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1740480661392212},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.13287290930747986},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1093/jigpal/jzm013","is_oa":false,"landing_page_url":"https://doi.org/10.1093/jigpal/jzm013","pdf_url":null,"source":{"id":"https://openalex.org/S2734381524","display_name":"Logic Journal of IGPL","issn_l":"1367-0751","issn":["1367-0751","1368-9894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logic Journal of IGPL","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education","score":0.5799999833106995}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W981129589","https://openalex.org/W1517012845","https://openalex.org/W2032357775","https://openalex.org/W2067332512","https://openalex.org/W2086177561"],"related_works":["https://openalex.org/W171744056","https://openalex.org/W1577881803","https://openalex.org/W3136886172","https://openalex.org/W2146906212","https://openalex.org/W4323354904","https://openalex.org/W2993442435","https://openalex.org/W2375826828","https://openalex.org/W4255069280","https://openalex.org/W1965300620","https://openalex.org/W1556336692"],"abstract_inverted_index":{"We":[0,93,116],"study":[1,95],"Basic":[2],"Arithmetic":[3,14,23],"BA,":[4],"which":[5,103],"is":[6,36,47,59,104],"the":[7,54,84,105,108,127],"basic":[8],"logic":[9,18,27],"BQC":[10],"equivalent":[11],"of":[12,21,53,64,69,74,78,88,99],"Heyting":[13],"HA":[15],"over":[16,25],"intuitionistic":[17],"IQC,":[19,125],"and":[20,126],"Peano":[22],"PA":[24,79],"classical":[26,72],"CQC.":[28],"It":[29],"turns":[30],"out":[31],"that":[32,45,61,118],"The":[33],"Friedman":[34],"translation":[35],"applicable":[37],"to":[38,83,124,133],"BA.":[39],"Using":[40],"this":[41,119],"translation,":[42],"we":[43],"prove":[44],"BA":[46,70],"closed":[48],"under":[49],"a":[50,65,76],"restricted":[51,82],"form":[52],"Markov":[55],"rule.":[56],"Moreover,":[57],"it":[58],"proved":[60],"all":[62],"nodes":[63],"finite":[66],"Kripke":[67],"model":[68],"are":[71],"models":[73],"I\u22031+\u2060,":[75],"fragment":[77],"with":[80],"Induction":[81],"formulas":[85],"made":[86],"up":[87],"\u2203,":[89],"\u2227":[90],"and/or":[91],"\u2228.":[92],"also":[94],"an":[96],"interesting":[97],"extension":[98,106,120],"BQC,":[100],"called":[101],"EBQC,":[102],"by":[107],"axiom":[109],"schema":[110],"\u22a4":[111],"\u2192":[112],"\u22a5":[113],"\u21d2":[114],"\u22a5.":[115],"show":[117],"behaves":[121],"very":[122],"like":[123],"corresponding":[128],"arithmetic,":[129],"EBA":[130],"shows":[131],"similarities":[132],"HA.":[134],"Mathematics":[135],"Subject":[136],"Classification:":[137],"Primary":[138],"03F30;":[139],"secondary":[140],"03F50.":[141]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}