{"id":"https://openalex.org/W2095873229","doi":"https://doi.org/10.2307/2271332","title":"Functions which remain partial recursive under all similarity transformations","display_name":"Functions which remain partial recursive under all similarity transformations","publication_year":1963,"publication_date":"1963-03-01","ids":{"openalex":"https://openalex.org/W2095873229","doi":"https://doi.org/10.2307/2271332","mag":"2095873229"},"language":"en","primary_location":{"id":"doi:10.2307/2271332","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2271332","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/A5025759793","display_name":"Norman Shapiro","orcid":null},"institutions":[{"id":"https://openalex.org/I1299303238","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88","country_code":"US","type":"government","lineage":["https://openalex.org/I1299022934","https://openalex.org/I1299303238"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Norman Shapiro","raw_affiliation_strings":["National Institutes of Health, Bethesda, Maryland","NATIONAL INSTITUTES OF HEALTH, BETHESDA, MARYLAND"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Institutes of Health, Bethesda, Maryland","institution_ids":["https://openalex.org/I1299303238"]},{"raw_affiliation_string":"NATIONAL INSTITUTES OF HEALTH, BETHESDA, MARYLAND","institution_ids":["https://openalex.org/I1299303238"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5025759793"],"corresponding_institution_ids":["https://openalex.org/I1299303238"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.26537433,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":"1","first_page":"17","last_page":"19"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12508","display_name":"Functional Equations Stability Results","score":0.9613999724388123,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T12508","display_name":"Functional Equations Stability Results","score":0.9613999724388123,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9587000012397766,"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":0.9513999819755554,"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/partial-function","display_name":"Partial function","score":0.7752748131752014},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.7678112983703613},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5969052314758301},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5545430183410645},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5085195302963257},{"id":"https://openalex.org/keywords/\u03bc-operator","display_name":"\u03bc operator","score":0.47546809911727905},{"id":"https://openalex.org/keywords/similarity","display_name":"Similarity (geometry)","score":0.43268924951553345},{"id":"https://openalex.org/keywords/recursive-functions","display_name":"Recursive functions","score":0.40699177980422974},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37481775879859924},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16745784878730774},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.15571093559265137},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09067633748054504},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.05173608660697937}],"concepts":[{"id":"https://openalex.org/C182359184","wikidata":"https://www.wikidata.org/wiki/Q1756942","display_name":"Partial function","level":2,"score":0.7752748131752014},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.7678112983703613},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5969052314758301},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5545430183410645},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5085195302963257},{"id":"https://openalex.org/C85955891","wikidata":"https://www.wikidata.org/wiki/Q307772","display_name":"\u03bc operator","level":3,"score":0.47546809911727905},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.43268924951553345},{"id":"https://openalex.org/C2982939207","wikidata":"https://www.wikidata.org/wiki/Q1175101","display_name":"Recursive functions","level":2,"score":0.40699177980422974},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37481775879859924},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16745784878730774},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.15571093559265137},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09067633748054504},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.05173608660697937},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2271332","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2271332","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"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183734623","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183734623","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"}],"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/W2065676782","https://openalex.org/W2191957727","https://openalex.org/W955824272","https://openalex.org/W1934005735","https://openalex.org/W1802255488","https://openalex.org/W2897159003","https://openalex.org/W2268847858","https://openalex.org/W1986019457","https://openalex.org/W2071312301","https://openalex.org/W2002433529"],"abstract_inverted_index":{"This":[0],"note":[1],"will":[2],"characterize":[3],"those":[4],"partial":[5,9,29,50],"functions":[6],"which":[7,52],"are":[8,58],"recursive":[10],"under":[11],"an":[12],"arbitrary":[13],"\u201crenaming\u201d":[14],"of":[15,42],"the":[16,24,49,56,73],"integers.":[17,26],"The":[18],"formal":[19],"result.":[20],"Let":[21],"I":[22,33,35,43],"be":[23,48],"non-negative":[25],"For":[27],"any":[28,39],"function":[30,51],"f":[31,46,53,67,76,91],"on":[32],"into":[34],",":[36,44],"and":[37],"for":[38],"permutation":[40],"\u03c3":[41,47,62,68,77,84],"let":[45,66],"becomes":[54],"when":[55],"integers":[57],"renamed":[59],"according":[60],"to":[61],".":[63,92],"That":[64],"is,":[65],"=":[69],"\u03c3f\u03c3":[70],"\u22121":[71,85],"in":[72],"sense":[74],"that":[75],"(":[78,86],"x":[79],")":[80,88],"is":[81],"defined":[82],"whenever":[83],"\u0445":[87],"\u220a":[89],"Dom":[90]},"counts_by_year":[],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}
