{"id":"https://openalex.org/W4206658284","doi":"https://doi.org/10.2307/2267457","title":"On the interpretation of non-finitist proofs\u2013Part II","display_name":"On the interpretation of non-finitist proofs\u2013Part II","publication_year":1952,"publication_date":"1952-03-01","ids":{"openalex":"https://openalex.org/W4206658284","doi":"https://doi.org/10.2307/2267457"},"language":"en","primary_location":{"id":"doi:10.2307/2267457","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2267457","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic 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/A5005951698","display_name":"G. Kreisel","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"G. Kreisel","raw_affiliation_strings":["The University, Reading, England"],"affiliations":[{"raw_affiliation_string":"The University, Reading, England","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5005951698"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":134,"citation_normalized_percentile":{"value":0.47424242,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"17","issue":"1","first_page":"43","last_page":"58"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.9922000169754028,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/T12170","display_name":"History and Theory of Mathematics","score":0.9922000169754028,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9884999990463257,"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":0.9794999957084656,"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/ackermann-function","display_name":"Ackermann function","score":0.9931056499481201},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.7361429929733276},{"id":"https://openalex.org/keywords/formalism","display_name":"Formalism (music)","score":0.6662124395370483},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.6260455846786499},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46648457646369934},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.42478781938552856},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.41207677125930786},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37877678871154785},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3784611225128174},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36285167932510376},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22255143523216248},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.12732645869255066},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08118149638175964}],"concepts":[{"id":"https://openalex.org/C33436860","wikidata":"https://www.wikidata.org/wiki/Q341835","display_name":"Ackermann function","level":3,"score":0.9931056499481201},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.7361429929733276},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.6662124395370483},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.6260455846786499},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46648457646369934},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.42478781938552856},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.41207677125930786},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37877678871154785},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3784611225128174},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36285167932510376},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22255143523216248},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.12732645869255066},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08118149638175964},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","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/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.0},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","level":1,"score":0.0},{"id":"https://openalex.org/C558565934","wikidata":"https://www.wikidata.org/wiki/Q2743","display_name":"Musical","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2307/2267457","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2267457","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2076743759","https://openalex.org/W4235144492","https://openalex.org/W2756792282","https://openalex.org/W2759493398","https://openalex.org/W2756744637","https://openalex.org/W2807877113","https://openalex.org/W4254767272","https://openalex.org/W2026076591","https://openalex.org/W2759073630","https://openalex.org/W4243761232"],"abstract_inverted_index":{"Since":[0],"the":[1,11,22,83,91],"Hilbert":[2],"substitution":[3],"method":[4],"has":[5],"been":[6],"applied":[7],"by":[8],"Ackermann":[9],"to":[10,45],"formalism":[12],"Z":[13,31,34],"of":[14,30,42,61,64,69,85],"number":[15],"theory":[16],"in":[17,57,90],"[3],":[18],"we":[19],"shall":[20],"give":[21],"no-counter-example":[23],"interpretation":[24],"for":[25],"extensions":[26],"(":[27,48,52,70,74],"c":[28],")":[29,50,72,76],",":[32],"e.g.":[33],"\u03bc":[35],".":[36],"The":[37,67],"work":[38],"required":[39],"on":[40],"top":[41],"Ackermann's":[43],"investigations":[44],"check":[46],"conditions":[47],"\u03b1":[49],"and":[51,73,81,88],"\u03b2":[53],"),":[54],"consists":[55],"only":[56],"a":[58,62],"suitable":[59],"definition":[60],"class":[63],"recursive":[65],"functional.":[66],"verification":[68],"\u03b3":[71],"\u03b4":[75],"is":[77],"much":[78],"more":[79],"difficult,":[80],"requires":[82],"ideas":[84],"paras.":[86],"32":[87],"33":[89],"preceding":[92],"section.":[93]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":11},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":6}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}