{"id":"https://openalex.org/W1977893559","doi":"https://doi.org/10.2178/bsl/1122038991","title":"Tiering as a Recursion Technique","display_name":"Tiering as a Recursion Technique","publication_year":2005,"publication_date":"2005-07-22","ids":{"openalex":"https://openalex.org/W1977893559","doi":"https://doi.org/10.2178/bsl/1122038991","mag":"1977893559"},"language":"en","primary_location":{"id":"doi:10.2178/bsl/1122038991","is_oa":false,"landing_page_url":"https://doi.org/10.2178/bsl/1122038991","pdf_url":null,"source":{"id":"https://openalex.org/S130801046","display_name":"Bulletin of Symbolic Logic","issn_l":"1079-8986","issn":["1079-8986","1943-5894"],"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":"Bulletin 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/A5049756356","display_name":"Harold Simmons","orcid":null},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Harold Simmons","raw_affiliation_strings":["Mathematical Foundations Group, The University of Manchester, Oxford Road, Manchester M13 9PL, England. E-mail:","Mathematical Foundations Group, The University of Manchester, Oxford Road, Manchester M13 9PL, England. E-mail/i: hsimmons@manchester.ac.uk"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Foundations Group, The University of Manchester, Oxford Road, Manchester M13 9PL, England. E-mail:","institution_ids":["https://openalex.org/I28407311"]},{"raw_affiliation_string":"Mathematical Foundations Group, The University of Manchester, Oxford Road, Manchester M13 9PL, England. E-mail/i: hsimmons@manchester.ac.uk","institution_ids":["https://openalex.org/I28407311"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5049756356"],"corresponding_institution_ids":["https://openalex.org/I28407311"],"apc_list":null,"apc_paid":null,"fwci":3.1551,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.91916473,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":93},"biblio":{"volume":"11","issue":"3","first_page":"321","last_page":"350"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9850999712944031,"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":0.9850999712944031,"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":0.9702000021934509,"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":0.9614999890327454,"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/recursion","display_name":"Recursion (computer science)","score":0.9589638113975525},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.6201090812683105},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5902029275894165},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5793079137802124},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4639745354652405},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.44710594415664673},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3403320908546448},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3392561674118042},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.31344932317733765},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20323210954666138},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13277015089988708},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.050992727279663086},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0386107861995697}],"concepts":[{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.9589638113975525},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.6201090812683105},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5902029275894165},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5793079137802124},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4639745354652405},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.44710594415664673},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3403320908546448},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3392561674118042},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.31344932317733765},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20323210954666138},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13277015089988708},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.050992727279663086},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0386107861995697}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2178/bsl/1122038991","is_oa":false,"landing_page_url":"https://doi.org/10.2178/bsl/1122038991","pdf_url":null,"source":{"id":"https://openalex.org/S130801046","display_name":"Bulletin of Symbolic Logic","issn_l":"1079-8986","issn":["1079-8986","1943-5894"],"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":"Bulletin of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.22.2686","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.22.2686","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.man.ac.uk/~hsimmons/PUBLICATIONS/DOCUMENTS/tiering.ps","raw_type":"text"},{"id":"pmh:oai:CULeuclid:euclid.bsl/1122038991","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.bsl/1122038991","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1539014","https://openalex.org/W636367345","https://openalex.org/W1520244229","https://openalex.org/W1560272532","https://openalex.org/W1654208522","https://openalex.org/W1969119492","https://openalex.org/W2013519208","https://openalex.org/W2034083013","https://openalex.org/W2034895188","https://openalex.org/W2062740098","https://openalex.org/W2069549740","https://openalex.org/W2069792094","https://openalex.org/W2149062436","https://openalex.org/W2334137773","https://openalex.org/W3022332613"],"related_works":["https://openalex.org/W1976679120","https://openalex.org/W4281614748","https://openalex.org/W2377519369","https://openalex.org/W30954630","https://openalex.org/W2765883196","https://openalex.org/W3202311233","https://openalex.org/W2034826746","https://openalex.org/W2396919090","https://openalex.org/W4251748586","https://openalex.org/W2477549100"],"abstract_inverted_index":{"Abstract":[0],"I":[1,20],"survey":[2],"the":[3,14,32],"syntactic":[4],"technique":[5],"of":[6,16,34,37],"tiering":[7],"which":[8],"can":[9,25],"be":[10,26],"used":[11],"to":[12],"restrict":[13],"power":[15],"a":[17,35],"recursion":[18],"scheme.":[19],"show":[21],"how":[22],"various":[23],"results":[24],"obtained":[27],"entirely":[28],"proof":[29],"theoretically":[30],"without":[31],"use":[33],"model":[36],"computation.":[38]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2025-10-10T00:00:00"}