{"id":"https://openalex.org/W1967612355","doi":"https://doi.org/10.1007/s001530050077","title":"Non-definability of the Ackermann function with type 1 partial primitive recursion","display_name":"Non-definability of the Ackermann function with type 1 partial primitive recursion","publication_year":1997,"publication_date":"1997-12-01","ids":{"openalex":"https://openalex.org/W1967612355","doi":"https://doi.org/10.1007/s001530050077","mag":"1967612355"},"language":"en","primary_location":{"id":"doi:10.1007/s001530050077","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s001530050077","pdf_url":null,"source":{"id":"https://openalex.org/S188076996","display_name":"Archive for Mathematical Logic","issn_l":"0933-5846","issn":["0933-5846","1432-0665"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Archive for Mathematical 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/A5113599640","display_name":"Karl-Heinz Niggl","orcid":null},"institutions":[{"id":"https://openalex.org/I8204097","display_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/05591te55","country_code":"DE","type":"education","lineage":["https://openalex.org/I8204097"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Karl-Heinz Niggl","raw_affiliation_strings":["Mathematisches Institut der Ludwig\u2013Maximilians\u2013Universit\u00e4t M\u00fcnchen, Theresienstrasse 39, D-80333 M\u00fcnchen, Germany\n, , , , , , DE","Mathematisches Institut der Ludwig\u2013Maximilians\u2013Universit\u00e4t M\u00fcnchen, Theresienstrasse 39, D-80333 M\u00fcnchen, Germany , DE"],"affiliations":[{"raw_affiliation_string":"Mathematisches Institut der Ludwig\u2013Maximilians\u2013Universit\u00e4t M\u00fcnchen, Theresienstrasse 39, D-80333 M\u00fcnchen, Germany\n, , , , , , DE","institution_ids":["https://openalex.org/I8204097"]},{"raw_affiliation_string":"Mathematisches Institut der Ludwig\u2013Maximilians\u2013Universit\u00e4t M\u00fcnchen, Theresienstrasse 39, D-80333 M\u00fcnchen, Germany , DE","institution_ids":["https://openalex.org/I8204097"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5113599640"],"corresponding_institution_ids":["https://openalex.org/I8204097"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":1.2081,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.81990859,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"37","issue":"1","first_page":"1","last_page":"13"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9987999796867371,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9987999796867371,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9984999895095825,"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/T11567","display_name":"semigroups and automata theory","score":0.9926000237464905,"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/ackermann-function","display_name":"Ackermann function","score":0.8445607423782349},{"id":"https://openalex.org/keywords/partial-function","display_name":"Partial function","score":0.7821749448776245},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7341379523277283},{"id":"https://openalex.org/keywords/double-recursion","display_name":"Double recursion","score":0.7311590909957886},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.6985435485839844},{"id":"https://openalex.org/keywords/primitive-recursive-function","display_name":"Primitive recursive function","score":0.5803812742233276},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5714487433433533},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5033707022666931},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.47327184677124023},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.41825157403945923},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40619957447052},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36509764194488525},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32109689712524414},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.08534041047096252}],"concepts":[{"id":"https://openalex.org/C33436860","wikidata":"https://www.wikidata.org/wiki/Q341835","display_name":"Ackermann function","level":3,"score":0.8445607423782349},{"id":"https://openalex.org/C182359184","wikidata":"https://www.wikidata.org/wiki/Q1756942","display_name":"Partial function","level":2,"score":0.7821749448776245},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7341379523277283},{"id":"https://openalex.org/C139503435","wikidata":"https://www.wikidata.org/wiki/Q5300083","display_name":"Double recursion","level":3,"score":0.7311590909957886},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.6985435485839844},{"id":"https://openalex.org/C9986523","wikidata":"https://www.wikidata.org/wiki/Q1570472","display_name":"Primitive recursive function","level":2,"score":0.5803812742233276},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5714487433433533},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5033707022666931},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.47327184677124023},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41825157403945923},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40619957447052},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36509764194488525},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32109689712524414},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.08534041047096252},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s001530050077","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s001530050077","pdf_url":null,"source":{"id":"https://openalex.org/S188076996","display_name":"Archive for Mathematical Logic","issn_l":"0933-5846","issn":["0933-5846","1432-0665"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Archive for Mathematical Logic","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.4099999964237213}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1526907582","https://openalex.org/W1539901982","https://openalex.org/W1544564247","https://openalex.org/W1608883294","https://openalex.org/W1680094959","https://openalex.org/W1719974439","https://openalex.org/W1987785781","https://openalex.org/W1988152122","https://openalex.org/W2041255733","https://openalex.org/W2085554469"],"related_works":["https://openalex.org/W1973821254","https://openalex.org/W2584778959","https://openalex.org/W2286072184","https://openalex.org/W4237768433","https://openalex.org/W2095450548","https://openalex.org/W2074941524","https://openalex.org/W4246540581","https://openalex.org/W1845597072","https://openalex.org/W1596057910","https://openalex.org/W2553341645"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}