{"id":"https://openalex.org/W2057691306","doi":"https://doi.org/10.1002/malq.19920380116","title":"ON THE ITERATED \u03c9\u2010RULE","display_name":"ON THE ITERATED \u03c9\u2010RULE","publication_year":1992,"publication_date":"1992-01-01","ids":{"openalex":"https://openalex.org/W2057691306","doi":"https://doi.org/10.1002/malq.19920380116","mag":"2057691306"},"language":"en","primary_location":{"id":"doi:10.1002/malq.19920380116","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19920380116","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","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/A5009745982","display_name":"Grzegorz Michalski","orcid":"https://orcid.org/0000-0002-8211-4057"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Grzegorz Michalski","raw_affiliation_strings":["Czerniakowska 30 m. 6 Warszawa 00-714 Poland","Czerniakowska 30 m. 6 Warszawa 00\u2010714 Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Czerniakowska 30 m. 6 Warszawa 00-714 Poland","institution_ids":[]},{"raw_affiliation_string":"Czerniakowska 30 m. 6 Warszawa 00\u2010714 Poland","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5009745982"],"corresponding_institution_ids":[],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.19877197,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"38","issue":"1","first_page":"203","last_page":"208"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9889000058174133,"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":0.9889000058174133,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9706000089645386,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9656999707221985,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8860499858856201},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.8532556295394897},{"id":"https://openalex.org/keywords/peano-axioms","display_name":"Peano axioms","score":0.8488024473190308},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6748993396759033},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.6324295997619629},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.5506722331047058},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5024476051330566},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4509427845478058},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06758129596710205},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06559708714485168}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8860499858856201},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.8532556295394897},{"id":"https://openalex.org/C97489613","wikidata":"https://www.wikidata.org/wiki/Q842755","display_name":"Peano axioms","level":2,"score":0.8488024473190308},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6748993396759033},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.6324295997619629},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5506722331047058},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5024476051330566},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4509427845478058},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06758129596710205},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06559708714485168},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/malq.19920380116","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19920380116","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W1008748165","https://openalex.org/W1988863058","https://openalex.org/W6647696822"],"related_works":["https://openalex.org/W4323354904","https://openalex.org/W2993442435","https://openalex.org/W2375826828","https://openalex.org/W4255069280","https://openalex.org/W1965300620","https://openalex.org/W2508096977","https://openalex.org/W2809575735","https://openalex.org/W4297813462","https://openalex.org/W1548936659","https://openalex.org/W3202246833"],"abstract_inverted_index":{"Abstract":[0],"Let":[1],"\u0393":[2,98],"n":[3,32,46,60,69,86,99,108,126,137,139],"(\u03c6)":[4,109],"be":[5],"a":[6,18],"formula":[7],"of":[8,20,39,42,78,93],"L":[9],"PA":[10,57],"(PA":[11],"=":[12],"Peano":[13],"Arithmetic)":[14],"meaning":[15],"\u201cthere":[16],"is":[17,27,90,112,123],"proof":[19],"\u03c6":[21,116],"from":[22,103],"PA\u2010axioms,":[23],"in":[24],"which":[25],"\u03c9\u2010rule":[26],"iterated":[28],"no":[29],"more":[30],"than":[31],"times\u201d.":[33],"We":[34],"examine":[35],"relations":[36],"over":[37],"pairs":[38],"natural":[40],"numbers":[41],"the":[43,79,91,94,104],"kind.":[44],"(":[45,52,62,70,87,125,132,145],",":[47,127],"k":[48,54,64,72,128,134,142],")":[49,66,89,129],"\u2266":[50,130,138,143],"H":[51,63,71,75,131],"n',":[53,133],"')":[55,135],"iff":[56],"+":[58,149],"RFN":[59,68,85],"'":[61,65,140,148],"\u22a9":[67],").":[73,119],"Where":[74],"denotes":[76],"one":[77],"hierarchies":[80],"\u2211":[81],"or":[82],"\u03a0":[83],"and":[84,141],"C":[88,106,118],"scheme":[92],"reflection":[95],"principle":[96],"for":[97,114],"restricted":[100],"to":[101],"formulas":[102],"class":[105],"(\u0393":[107],"implies":[110],"\u201c\u03c6":[111],"true\u201d,":[113],"every":[115],"\u2208":[117],"Our":[120],"main":[121],"result":[122],"that.":[124],"if":[136],"max":[144],"k',":[146],"2n":[147],"1).":[150]},"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}