{"id":"https://openalex.org/W2118174451","doi":"https://doi.org/10.1002/malq.19970430208","title":"Some Hierarchies of Primitive Recursive Functions on Term Algebras","display_name":"Some Hierarchies of Primitive Recursive Functions on Term Algebras","publication_year":1997,"publication_date":"1997-01-01","ids":{"openalex":"https://openalex.org/W2118174451","doi":"https://doi.org/10.1002/malq.19970430208","mag":"2118174451"},"language":"en","primary_location":{"id":"doi:10.1002/malq.19970430208","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19970430208","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","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/A5066286347","display_name":"Klaus\u2010Hilmar Sprenger","orcid":null},"institutions":[{"id":"https://openalex.org/I2800742272","display_name":"Folkwang University of the Arts","ror":"https://ror.org/03gf02c22","country_code":"DE","type":"education","lineage":["https://openalex.org/I2800742272"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Klaus\u2010Hilmar Sprenger","raw_affiliation_strings":["Theoretische Informatik, Fachbereich Mathematik, Universita\u0308t-GH Siegen, D-57068 Siegen, Germany","This paper contains the results of my Ph.D. dissertation [31], where most of the proofs which could only be sketched here can be found. Thanks go to my adviser, Prof. Dieter Spreen, who enabled me to carry through this project \u2013 under liberal and comfortable working conditions. Without his support this work would not have been possible. Andreas Weiermann and Klaus Weihrauch gave me access to unpublished, but important literature"],"affiliations":[{"raw_affiliation_string":"Theoretische Informatik, Fachbereich Mathematik, Universita\u0308t-GH Siegen, D-57068 Siegen, Germany","institution_ids":["https://openalex.org/I2800742272"]},{"raw_affiliation_string":"This paper contains the results of my Ph.D. dissertation [31], where most of the proofs which could only be sketched here can be found. Thanks go to my adviser, Prof. Dieter Spreen, who enabled me to carry through this project \u2013 under liberal and comfortable working conditions. Without his support this work would not have been possible. Andreas Weiermann and Klaus Weihrauch gave me access to unpublished, but important literature","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5066286347"],"corresponding_institution_ids":["https://openalex.org/I2800742272"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.23299676,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"43","issue":"2","first_page":"251","last_page":"286"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9955999851226807,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9955999851226807,"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":0.994700014591217,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9925000071525574,"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/mathematics","display_name":"Mathematics","score":0.8609007596969604},{"id":"https://openalex.org/keywords/primitive-recursive-function","display_name":"Primitive recursive function","score":0.7862842082977295},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.7191802263259888},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.6146664619445801},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.5469378232955933},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.46028581261634827},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.4324629008769989},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4253597557544708},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4084995985031128},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.35802793502807617}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8609007596969604},{"id":"https://openalex.org/C9986523","wikidata":"https://www.wikidata.org/wiki/Q1570472","display_name":"Primitive recursive function","level":2,"score":0.7862842082977295},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.7191802263259888},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.6146664619445801},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.5469378232955933},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.46028581261634827},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.4324629008769989},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4253597557544708},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4084995985031128},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.35802793502807617},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/malq.19970430208","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19970430208","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.7400000095367432,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W103704919","https://openalex.org/W114307860","https://openalex.org/W117031590","https://openalex.org/W613056435","https://openalex.org/W658109713","https://openalex.org/W1481367701","https://openalex.org/W1549823126","https://openalex.org/W1572576657","https://openalex.org/W1579247651","https://openalex.org/W1964956087","https://openalex.org/W1981324778","https://openalex.org/W1984196604","https://openalex.org/W1988826480","https://openalex.org/W1997775866","https://openalex.org/W1999590237","https://openalex.org/W2007804326","https://openalex.org/W2018632099","https://openalex.org/W2020959464","https://openalex.org/W2025998521","https://openalex.org/W2055303025","https://openalex.org/W2069227855","https://openalex.org/W2075188242","https://openalex.org/W2085554469","https://openalex.org/W2574999163","https://openalex.org/W3023466934"],"related_works":["https://openalex.org/W1996792588","https://openalex.org/W2074941524","https://openalex.org/W2584778959","https://openalex.org/W1596057910","https://openalex.org/W3102439663","https://openalex.org/W2167424714","https://openalex.org/W4388322088","https://openalex.org/W252215219","https://openalex.org/W1845597072","https://openalex.org/W2359098868"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"compare":[2],"two":[3],"different":[4],"Grzegorczyk":[5,45,74],"hierarchies":[6],"{":[7,15,64,78,95,111],"H":[8,65],"n":[9,12,17,20,54,58,66,69,80,83,97,100,113,116],"\u03c3":[10,18,55,59,67,98,114,124],"}":[11,19,68,82,99,115,125],"\u22650":[13,70,84,117],"and":[14,31,47,56,132,148],"L":[16,96,122],"\u22651":[21,101],"on":[22,60,76,118],"term":[23,61,87,136,145],"algebras,":[24],"which":[25],"grow":[26],"according":[27],"to":[28,71,85,104,108,128],"the":[29,44,48,119],"height":[30],"length":[32],"of":[33,38,143],"terms,":[34],"respectively.":[35],"The":[36],"solution":[37],"almost":[39],"all":[40],"inclusion":[41],"problems":[42],"among":[43],"classes":[46,52],"(simultaneous)":[49],"recursion":[50],"number":[51],"R":[53],"S":[57],"algebras":[62],"shows":[63],"generalize":[72],"Weihrauch's":[73,109],"hierarchy":[75,110],"words":[77],"E":[79,112],"k":[81],"arbitrary":[86],"algebras.":[88],"However,":[89],"by":[90],"regarding":[91],"terms":[92],"as":[93],"words,":[94],"turns":[102],"out":[103],"be":[105],"computationally":[106],"equivalent":[107,127],"whole.":[120],"Especially,":[121],"2":[123],"is":[126],"polynomial":[129],"time":[130],"computability":[131],"contains":[133],"several":[134],"natural":[135],"algebra":[137,146],"functions.":[138],"This":[139],"establishes":[140],"a":[141],"notion":[142],"feasible":[144],"functions":[147],"predicates.":[149]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}