{"id":"https://openalex.org/W7125943761","doi":"https://doi.org/10.1093/logcom/exaf070","title":"The Ackermann encoding and its siblings","display_name":"The Ackermann encoding and its siblings","publication_year":2025,"publication_date":"2025-11-11","ids":{"openalex":"https://openalex.org/W7125943761","doi":"https://doi.org/10.1093/logcom/exaf070"},"language":"en","primary_location":{"id":"doi:10.1093/logcom/exaf070","is_oa":false,"landing_page_url":"https://doi.org/10.1093/logcom/exaf070","pdf_url":null,"source":{"id":"https://openalex.org/S47057106","display_name":"Journal of Logic and Computation","issn_l":"0955-792X","issn":["0955-792X","1465-363X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Logic and Computation","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/A5124098184","display_name":"Simone Boscaratto","orcid":null},"institutions":[{"id":"https://openalex.org/I129043915","display_name":"University of Udine","ror":"https://ror.org/05ht0mh31","country_code":"IT","type":"education","lineage":["https://openalex.org/I129043915"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Simone Boscaratto","raw_affiliation_strings":["Dipartimento di Matematica, Informatica e Fisica, Universit\u00e0 degli Studi di Udine , Via delle Scienze, 206, 33100 Udine ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Informatica e Fisica, Universit\u00e0 degli Studi di Udine , Via delle Scienze, 206, 33100 Udine ,","institution_ids":["https://openalex.org/I129043915"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045684463","display_name":"Domenico Cantone","orcid":"https://orcid.org/0000-0002-1306-1166"},"institutions":[{"id":"https://openalex.org/I39063666","display_name":"University of Catania","ror":"https://ror.org/03a64bh57","country_code":"IT","type":"education","lineage":["https://openalex.org/I39063666"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Domenico Cantone","raw_affiliation_strings":["Dipartimento di Matematica e Informatica, Universit\u00e0 degli Studi di Catania , Viale Andrea Doria, 6, 95125 Catania ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica e Informatica, Universit\u00e0 degli Studi di Catania , Viale Andrea Doria, 6, 95125 Catania ,","institution_ids":["https://openalex.org/I39063666"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050863922","display_name":"Eugenio G. Omodeo","orcid":"https://orcid.org/0000-0003-3917-1942"},"institutions":[{"id":"https://openalex.org/I142444530","display_name":"University of Trieste","ror":"https://ror.org/02n742c10","country_code":"IT","type":"education","lineage":["https://openalex.org/I142444530"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Eugenio G Omodeo","raw_affiliation_strings":["Dipartimento di Matematica, Informatica e Geoscienze, Universit\u00e0 degli Studi di Trieste , Via Valerio, 12/1, 34127 Trieste ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Informatica e Geoscienze, Universit\u00e0 degli Studi di Trieste , Via Valerio, 12/1, 34127 Trieste ,","institution_ids":["https://openalex.org/I142444530"]}]},{"author_position":"last","author":{"id":null,"display_name":"Alberto Policriti","orcid":null},"institutions":[{"id":"https://openalex.org/I129043915","display_name":"University of Udine","ror":"https://ror.org/05ht0mh31","country_code":"IT","type":"education","lineage":["https://openalex.org/I129043915"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Alberto Policriti","raw_affiliation_strings":["Dipartimento di Matematica, Informatica e Fisica, Universit\u00e0 degli Studi di Udine , Via delle Scienze, 206, 33100 Udine ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Informatica e Fisica, Universit\u00e0 degli Studi di Udine , Via delle Scienze, 206, 33100 Udine ,","institution_ids":["https://openalex.org/I129043915"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":4151,"currency":"USD","value_usd":4151},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.82501959,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"36","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.0997999981045723,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.0997999981045723,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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":0.09709999710321426,"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/T11797","display_name":"graph theory and CDMA systems","score":0.07190000265836716,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ackermann-function","display_name":"Ackermann function","score":0.9233999848365784},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.7620999813079834},{"id":"https://openalex.org/keywords/injective-function","display_name":"Injective function","score":0.6358000040054321},{"id":"https://openalex.org/keywords/encoding","display_name":"Encoding (memory)","score":0.5733000040054321},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.47130000591278076},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4332999885082245},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.4097999930381775}],"concepts":[{"id":"https://openalex.org/C33436860","wikidata":"https://www.wikidata.org/wiki/Q341835","display_name":"Ackermann function","level":3,"score":0.9233999848365784},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.7620999813079834},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6952999830245972},{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.6358000040054321},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.5733000040054321},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49779999256134033},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.48969998955726624},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.47130000591278076},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4332999885082245},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4097999930381775},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.40310001373291016},{"id":"https://openalex.org/C188370112","wikidata":"https://www.wikidata.org/wiki/Q173091","display_name":"Transcendental number","level":2,"score":0.38839998841285706},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.3578000068664551},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3199999928474426},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.31349998712539673},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.2578999996185303},{"id":"https://openalex.org/C2778692605","wikidata":"https://www.wikidata.org/wiki/Q4041866","display_name":"Joins","level":2,"score":0.2565000057220459},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.25459998846054077}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1093/logcom/exaf070","is_oa":false,"landing_page_url":"https://doi.org/10.1093/logcom/exaf070","pdf_url":null,"source":{"id":"https://openalex.org/S47057106","display_name":"Journal of Logic and Computation","issn_l":"0955-792X","issn":["0955-792X","1465-363X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Logic and Computation","raw_type":"journal-article"},{"id":"pmh:oai:air.uniud.it:11390/1314309","is_oa":false,"landing_page_url":"https://hdl.handle.net/11390/1314309","pdf_url":null,"source":{"id":"https://openalex.org/S4306401163","display_name":"Institutional Research Information System (University of Udine)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I129043915","host_organization_name":"University of Udine","host_organization_lineage":["https://openalex.org/I129043915"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:arts.units.it:11368/3128518","is_oa":false,"landing_page_url":"https://hdl.handle.net/11368/3128518","pdf_url":null,"source":{"id":"https://openalex.org/S4306400480","display_name":"ArTS Archivio della ricerca di Trieste (University of Trieste https://www.units.it/)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142444530","host_organization_name":"University of Trieste","host_organization_lineage":["https://openalex.org/I142444530"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.4539083242416382,"display_name":"Reduced inequalities"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320322690","display_name":"Universit\u00e0 di Catania","ror":"https://ror.org/03a64bh57"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1657826747","https://openalex.org/W2007983321","https://openalex.org/W2014030742","https://openalex.org/W2068361557","https://openalex.org/W2068728923","https://openalex.org/W2083347756","https://openalex.org/W2084340327","https://openalex.org/W2124325155","https://openalex.org/W2124875712","https://openalex.org/W2157750270","https://openalex.org/W2176114185","https://openalex.org/W2913482449","https://openalex.org/W2951311167","https://openalex.org/W4206007682","https://openalex.org/W4214710890","https://openalex.org/W4240199913","https://openalex.org/W4246447829","https://openalex.org/W4252514983","https://openalex.org/W4254997534","https://openalex.org/W6960227003","https://openalex.org/W6960227826"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"The":[1],"celebrated":[2],"Ackermann":[3,67],"encoding":[4,68,92,132],"of":[5,52,61,93,96,133],"hereditarily":[6,24,97],"finite":[7,25,98],"sets":[8,21],"is":[9,81,108,126],"generalized":[10],"to":[11,16,40,48,110,128],"a":[12,37,49,90,94,116],"parametric":[13],"formula":[14],"designed":[15],"map":[17,73],"not":[18],"only":[19],"these":[20],"but":[22],"also":[23],"multisets":[26,99,135],"and":[27,69,113,136],"hypersets":[28],"into":[29,100],"the":[30,41,58,65,79,84,87,101,106,120,124],"non-negative":[31],"real":[32,53,122],"numbers.":[33,103],"This":[34],"extension":[35],"suggests":[36],"novel":[38],"approach":[39],"graph":[42],"canonization":[43],"problem":[44],"by":[45],"reducing":[46],"it":[47],"simple":[50],"comparison":[51],"values.":[54],"By":[55],"suitably":[56],"varying":[57],"sole":[59],"parameter":[60,80,107],"this":[62],"formula,":[63],"both":[64,134],"original":[66],"another":[70],"previously":[71],"studied":[72],"emerge":[74],"as":[75],"special":[76],"cases.":[77],"When":[78],"chosen":[82,109],"from":[83],"natural":[85,102],"numbers,":[86],"function":[88,125],"yields":[89],"bijective":[91],"subuniverse":[95],"If,":[104],"instead,":[105],"be":[111],"transcendental":[112],"lies":[114],"within":[115],"specific":[117],"interval":[118],"on":[119],"positive":[121],"line,":[123],"conjectured":[127],"provide":[129],"an":[130],"injective":[131],"hypersets.":[137]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-01-29T00:00:00"}
