{"id":"https://openalex.org/W201390185","doi":null,"title":"Axioms and theorems for integers, lists and finite sets in LCF.","display_name":"Axioms and theorems for integers, lists and finite sets in LCF.","publication_year":1973,"publication_date":"1973-01-01","ids":{"openalex":"https://openalex.org/W201390185","mag":"201390185"},"language":"en","primary_location":{"id":"mag:201390185","doi":null,"is_oa":false,"landing_page_url":"https://dl.acm.org/citation.cfm?id=891976","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"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/A5111374653","display_name":"Malcolm C. Newey","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Malcolm C. Newey","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5111374653"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8464,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.86538462,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":93},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"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/T10126","display_name":"Logic, programming, and type systems","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"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":0.000699999975040555,"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/T10142","display_name":"Formal Methods in Verification","score":9.999999747378752e-05,"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/low-cycle-fatigue","display_name":"low cycle fatigue","score":0.8040000200271606},{"id":"https://openalex.org/keywords/formalization-of-mathematics","display_name":"mathematical formalization","score":0.492000013589859},{"id":"https://openalex.org/keywords/axiomatic-foundations","display_name":"axiomatic foundations","score":0.7509999871253967},{"id":"https://openalex.org/keywords/integer-arithmetic","display_name":"integer arithmetic","score":0.9800000190734863},{"id":"https://openalex.org/keywords/list-manipulation","display_name":"list manipulation","score":0.9810000061988831},{"id":"https://openalex.org/keywords/proof-verification","display_name":"proof verification","score":0.6769999861717224},{"id":"https://openalex.org/keywords/mathematical-theory-of-computation","display_name":"mathematical theory of computation","score":0.8759999871253967}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.8982138633728027},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.8022596836090088},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5486819744110107},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5451502203941345},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5343610048294067},{"id":"https://openalex.org/C47884741","wikidata":"https://www.wikidata.org/wiki/Q1166618","display_name":"Mathematical logic","level":2,"score":0.4873093366622925},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4621966481208801},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.45746737718582153},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4528549313545227},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.447500616312027},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.4447585940361023},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.4218013882637024},{"id":"https://openalex.org/C54271186","wikidata":"https://www.wikidata.org/wiki/Q1148456","display_name":"Computable function","level":2,"score":0.4139844477176666},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36949393153190613},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2328759729862213},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.21861562132835388},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.17823302745819092},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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},{"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":"mag:201390185","doi":null,"is_oa":false,"landing_page_url":"https://dl.acm.org/citation.cfm?id=891976","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":1,"referenced_works":["https://openalex.org/W2094015376"],"related_works":["https://openalex.org/W330865555","https://openalex.org/W1741698332","https://openalex.org/W1537108372","https://openalex.org/W321365057","https://openalex.org/W2022351728","https://openalex.org/W6891524706","https://openalex.org/W3026552755","https://openalex.org/W2798789889","https://openalex.org/W1968333039","https://openalex.org/W1991293669"],"abstract_inverted_index":{"LCF":[0,44,89],"(Logic":[1],"for":[2,13,87,100],"Computable":[3],"Functions)":[4],"is":[5],"being":[6],"promoted":[7],"as":[8],"a":[9,53,83,105],"formal":[10],"language":[11],"suitable":[12,84],"the":[14,20,43,59,74,111],"discussion":[15],"of":[16,23,31,56,73,104,108,113],"various":[17],"problems":[18,33],"in":[19,47,58],"Mathematical":[21],"Theory":[22],"Computation":[24],"(MTC).":[25],"To":[26],"this":[27],"end,":[28],"several":[29],"examples":[30],"MTC":[32],"have":[34,39,65],"been":[35,40,52,66],"formalised":[36],"and":[37,70,91,118],"proofs":[38],"exhibited":[41],"using":[42],"proof-checker.":[45],"However,":[46],"these":[48],"examples,":[49],"there":[50],"has":[51],"certain":[54],"amount":[55],"ad-hoc-ery":[57],"proofs;":[60],"namely,":[61],"many":[62],"mathematical":[63,75,85],"theorems":[64,109],"assumed":[67],"without":[68],"proof":[69],"no":[71],"axiomatisation":[72],"domains":[76],"involved":[77],"was":[78],"given.":[79],"This":[80],"paper":[81],"describes":[82],"environment":[86,96],"future":[88],"experiments":[90],"its":[92],"axiomatic":[93],"basis.":[94],"The":[95],"developed,":[97],"deemed":[98],"appropriate":[99],"such":[101],"experiments,":[102],"consists":[103],"large":[106],"body":[107],"from":[110],"areas":[112],"integer":[114],"arithmetic,":[115],"list":[116],"manipulation":[117],"finite":[119],"set":[120],"theory.":[121]},"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T04:12:42.849631","created_date":"2016-06-24T00:00:00"}
