{"id":"https://openalex.org/W1980566306","doi":"https://doi.org/10.1017/s0022481200051598","title":"The infinite injury priority method","display_name":"The infinite injury priority method","publication_year":1976,"publication_date":"1976-06-01","ids":{"openalex":"https://openalex.org/W1980566306","doi":"https://doi.org/10.1017/s0022481200051598","mag":"1980566306"},"language":"en","primary_location":{"id":"doi:10.1017/s0022481200051598","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0022481200051598","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"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":"Journal 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/A5023422267","display_name":"Robert I. Soare","orcid":null},"institutions":[{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]},{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Robert I. Soare","raw_affiliation_strings":["University of Chicago, Chicago, Illinois 60637","University of Illinois, Chicago Circle, Illinois 60680"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Chicago, Chicago, Illinois 60637","institution_ids":["https://openalex.org/I40347166"]},{"raw_affiliation_string":"University of Illinois, Chicago Circle, Illinois 60680","institution_ids":["https://openalex.org/I39422238"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5023422267"],"corresponding_institution_ids":["https://openalex.org/I39422238","https://openalex.org/I40347166"],"apc_list":null,"apc_paid":null,"fwci":2.964,"has_fulltext":false,"cited_by_count":48,"citation_normalized_percentile":{"value":0.90477299,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"41","issue":"2","first_page":"513","last_page":"530"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9491000175476074,"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/T10142","display_name":"Formal Methods in Verification","score":0.9491000175476074,"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":0.9376999735832214,"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":0.919700026512146,"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/mathematical-proof","display_name":"Mathematical proof","score":0.6998054385185242},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.6676508188247681},{"id":"https://openalex.org/keywords/recursively-enumerable-language","display_name":"Recursively enumerable language","score":0.6380084156990051},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.5928503274917603},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5543599724769592},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5338172912597656},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49280789494514465},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46181073784828186},{"id":"https://openalex.org/keywords/action","display_name":"Action (physics)","score":0.45050692558288574},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4377664625644684},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4327084422111511},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.27737265825271606},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09972694516181946},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.07446467876434326}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6998054385185242},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.6676508188247681},{"id":"https://openalex.org/C203702658","wikidata":"https://www.wikidata.org/wiki/Q1073063","display_name":"Recursively enumerable language","level":2,"score":0.6380084156990051},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.5928503274917603},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5543599724769592},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5338172912597656},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49280789494514465},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46181073784828186},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.45050692558288574},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4377664625644684},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4327084422111511},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27737265825271606},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09972694516181946},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.07446467876434326},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1017/s0022481200051598","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0022481200051598","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"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":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183739794","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183739794","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.360.4499","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.360.4499","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.umd.edu/~gasarch/BLOGPAPERS/infinj.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.5099999904632568}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W44111308","https://openalex.org/W183106294","https://openalex.org/W1268767236","https://openalex.org/W1579907443","https://openalex.org/W1965251765","https://openalex.org/W1971553070","https://openalex.org/W1972685794","https://openalex.org/W1975466840","https://openalex.org/W2006726677","https://openalex.org/W2015965037","https://openalex.org/W2029823283","https://openalex.org/W2036225116","https://openalex.org/W2037416374","https://openalex.org/W2070390550","https://openalex.org/W2082637799","https://openalex.org/W2101746971","https://openalex.org/W2117832390","https://openalex.org/W2285371954","https://openalex.org/W2315181607","https://openalex.org/W2320833443","https://openalex.org/W2530006810","https://openalex.org/W2905135108","https://openalex.org/W4249457683"],"related_works":["https://openalex.org/W2072965782","https://openalex.org/W2132512348","https://openalex.org/W2140918173","https://openalex.org/W2132951762","https://openalex.org/W2000487993","https://openalex.org/W54673772","https://openalex.org/W1998171255","https://openalex.org/W4221036368","https://openalex.org/W2963684594","https://openalex.org/W2467957161"],"abstract_inverted_index":{"One":[0],"of":[1,31,79,179,200,207,240,262,269,279],"the":[2,13,77,110,149,195,213,227,238,258,263],"most":[3,118],"important":[4],"and":[5,56,99,106,125,130,148,153,162,174,182,245,249],"distinctive":[6],"tools":[7],"in":[8,139,253],"recursion":[9],"theory":[10],"has":[11,188],"been":[12,190],"priority":[14,52,92],"method":[15,93,138,150,187,198,215,264],"whereby":[16],"a":[17,29,68,134,141,254,276],"recursively":[18],"enumerable":[19],"(r.e.)":[20],"set":[21],"A":[22],"is":[23,50,107,115,210,265,273],"constructed":[24],"by":[25,96,109,155,247],"stages":[26],"to":[27,102,166,211,216,226,257],"satisfy":[28],"sequence":[30],"conditions":[32],"{":[33],"R":[34,48,54,60,80,84],"n":[35,37,43,49,81],"}":[36],"\u2208\u03c9":[38],"called":[39],"requirements":[40],".":[41,89],"If":[42],"&lt;":[44],"m":[45,55,61,85],",":[46],"requirement":[47,114,142],"given":[51],"over":[53],"action":[57],"taken":[58],"for":[59,76],"at":[62,67,86,117],"some":[63,246],"stage":[64,70,87],"s":[65,73],"may":[66,143],"later":[69],"t":[71,88],"&gt;":[72],"be":[74,144],"undone":[75],"sake":[78],"thereby":[82],"injuring":[83],"The":[90,205,260],"first":[91],"was":[94,151],"invented":[95,133],"Friedberg":[97],"[2]":[98],"Muchnik":[100],"[11]":[101],"solve":[103],"Post's":[104],"problem":[105],"characterized":[108],"fact":[111],"that":[112],"each":[113],"injured":[116,145],"finitely":[119],"often.":[120],"Shoenfield":[121],"[20,":[122],"Lemma":[123],"1],":[124],"then":[126],"independently":[127],"Sacks":[128,156,214,241],"[17]":[129],"Yates":[131,163,248],"[25]":[132],"much":[135],"more":[136],"powerful":[137],"which":[140,272],"infinitely":[146],"often,":[147],"applied":[152],"refined":[154],"[15],":[157],"[16],":[158],"[17],":[159],"[18],":[160],"[19]":[161],"[25],":[164],"[26]":[165],"obtain":[167],"many":[168],"deep":[169],"results":[170,239],"on":[171,242],"r.e.":[172,243],"sets":[173],"their":[175],"degrees.":[176],"In":[177],"spite":[178],"numerous":[180],"simplifications":[181],"variations":[183],"this":[184,208],"infinite":[185],"injury":[186,197,229],"never":[189],"as":[191,194,251],"well":[192],"understood":[193,219],"finite":[196,228],"because":[199],"its":[201],"apparently":[202],"greater":[203],"complexity.":[204],"purpose":[206],"paper":[209],"reduce":[212],"two":[217],"easily":[218],"lemmas":[220,233],"whose":[221],"proofs":[222],"are":[223],"very":[224],"similar":[225],"case.":[230],"Using":[231],"these":[232],"we":[234],"can":[235],"derive":[236],"all":[237],"degrees,":[244],"Robinson":[250],"well,":[252],"manner":[255],"accessible":[256],"nonspecialist.":[259],"heart":[261],"an":[266],"ingenious":[267],"observation":[268],"Lachlan":[270],"[7]":[271],"combined":[274],"with":[275],"further":[277],"simplification":[278],"our":[280],"own.":[281]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
