{"id":"https://openalex.org/W2075443053","doi":"https://doi.org/10.1305/ndjfl/1039724890","title":"A Conjecture on Numeral Systems","display_name":"A Conjecture on Numeral Systems","publication_year":1997,"publication_date":"1997-04-01","ids":{"openalex":"https://openalex.org/W2075443053","doi":"https://doi.org/10.1305/ndjfl/1039724890","mag":"2075443053"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1039724890","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1039724890","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-38/issue-2/A-Conjecture-on-Numeral-Systems/10.1305/ndjfl/1039724890.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-38/issue-2/A-Conjecture-on-Numeral-Systems/10.1305/ndjfl/1039724890.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018831581","display_name":"Karim Nour","orcid":"https://orcid.org/0000-0003-1943-272X"},"institutions":[{"id":"https://openalex.org/I4210155549","display_name":"Laboratoire de Math\u00e9matiques","ror":"https://ror.org/05sd5r855","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I198244214","https://openalex.org/I4210141950","https://openalex.org/I4210155549"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Karim Nour","raw_affiliation_strings":["Laboratoire de Math\u00e9matiques"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de Math\u00e9matiques","institution_ids":["https://openalex.org/I4210155549"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5018831581"],"corresponding_institution_ids":["https://openalex.org/I4210155549"],"apc_list":null,"apc_paid":null,"fwci":0.518,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.67159844,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"38","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9941999912261963,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9941999912261963,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.98580002784729,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9750999808311462,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/numeral-system","display_name":"Numeral system","score":0.882611870765686},{"id":"https://openalex.org/keywords/unary-operation","display_name":"Unary operation","score":0.8785743117332458},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7191410064697266},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7107784748077393},{"id":"https://openalex.org/keywords/successor-cardinal","display_name":"Successor cardinal","score":0.634338915348053},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5546221733093262},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4999823570251465},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.44804441928863525},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.4188937544822693},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4121484160423279},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37906521558761597},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22038128972053528},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06375834345817566},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.0569625198841095},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.05602431297302246}],"concepts":[{"id":"https://openalex.org/C204160518","wikidata":"https://www.wikidata.org/wiki/Q122653","display_name":"Numeral system","level":2,"score":0.882611870765686},{"id":"https://openalex.org/C78023250","wikidata":"https://www.wikidata.org/wiki/Q657596","display_name":"Unary operation","level":2,"score":0.8785743117332458},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7191410064697266},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7107784748077393},{"id":"https://openalex.org/C75306776","wikidata":"https://www.wikidata.org/wiki/Q7632662","display_name":"Successor cardinal","level":2,"score":0.634338915348053},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5546221733093262},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4999823570251465},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.44804441928863525},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4188937544822693},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4121484160423279},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37906521558761597},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22038128972053528},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06375834345817566},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0569625198841095},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.05602431297302246},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1305/ndjfl/1039724890","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1039724890","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-38/issue-2/A-Conjecture-on-Numeral-Systems/10.1305/ndjfl/1039724890.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:0905.0755","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0905.0755","pdf_url":"https://arxiv.org/pdf/0905.0755","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:CULeuclid:euclid.ndjfl/1039724890","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.ndjfl/1039724890","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.250.7268","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.250.7268","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0905.0755v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.97.3419","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.97.3419","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.lama.univ-savoie.fr/~nour/conjNS.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00381596v1","is_oa":false,"landing_page_url":"https://hal.science/hal-00381596","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Notre Dame Journal of Formal Logic, 1997, 38, pp.270-275","raw_type":"Journal articles"}],"best_oa_location":{"id":"doi:10.1305/ndjfl/1039724890","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1039724890","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-38/issue-2/A-Conjecture-on-Numeral-Systems/10.1305/ndjfl/1039724890.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2075443053.pdf","grobid_xml":"https://content.openalex.org/works/W2075443053.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W1976556784","https://openalex.org/W2088979440","https://openalex.org/W2154273644","https://openalex.org/W2963854355","https://openalex.org/W6637737520"],"related_works":["https://openalex.org/W2473542051","https://openalex.org/W3123320268","https://openalex.org/W2994519609","https://openalex.org/W2726593096","https://openalex.org/W2054269721","https://openalex.org/W4235459050","https://openalex.org/W2767501615","https://openalex.org/W2390822611","https://openalex.org/W2888918612","https://openalex.org/W2789953504"],"abstract_inverted_index":{"A":[0],"numeral":[1,29],"system":[2],"is":[3],"an":[4],"infinite":[5],"sequence":[6],"of":[7,53,68],"different":[8],"closed":[9],"normal":[10],"$\\lambda$-terms":[11],"intended":[12],"to":[13,72],"code":[14],"the":[15,31,51,61,66],"integers":[16],"in":[17],"$\\lambda$-calculus.":[18],"Barendregt":[19],"has":[20],"shown":[21],"that":[22],"if":[23],"we":[24,49],"can":[25,43],"represent,":[26],"for":[27],"a":[28,63],"system,":[30],"functions":[32,42,70],"Successor,":[33],"Predecessor,":[34],"and":[35],"Zero":[36],"Test,":[37],"then":[38],"all":[39,74],"total":[40,75],"recursive":[41,76],"be":[44],"represented.":[45],"In":[46],"this":[47],"paper":[48],"prove":[50],"independancy":[52],"these":[54],"three":[55],"particular":[56],"functions.":[57,77],"We":[58],"give":[59],"at":[60],"end":[62],"conjecture":[64],"on":[65],"number":[67],"unary":[69],"necessary":[71],"represent":[73]},"counts_by_year":[],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2025-10-10T00:00:00"}
