{"id":"https://openalex.org/W2163888089","doi":"https://doi.org/10.2307/2272316","title":"The pure part of HYP(\u2133)","display_name":"The pure part of HYP(\u2133)","publication_year":1977,"publication_date":"1977-03-01","ids":{"openalex":"https://openalex.org/W2163888089","doi":"https://doi.org/10.2307/2272316","mag":"2163888089"},"language":"en","primary_location":{"id":"doi:10.2307/2272316","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2272316","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/A5074274651","display_name":"Mark Nadel","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mark Nadel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5019899729","display_name":"Jonathan Stavi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jonathan Stavi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6414,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.70552434,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"42","issue":"1","first_page":"33","last_page":"46"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9973000288009644,"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/T11567","display_name":"semigroups and automata theory","score":0.9973000288009644,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9866999983787537,"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/T10181","display_name":"Natural Language Processing Techniques","score":0.9599000215530396,"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/countable-set","display_name":"Countable set","score":0.9212269186973572},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7031558752059937},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6771180033683777},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.6624709367752075},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5843191146850586},{"id":"https://openalex.org/keywords/quantifier","display_name":"Quantifier (linguistics)","score":0.5725892782211304},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.49900221824645996},{"id":"https://openalex.org/keywords/quantifier-elimination","display_name":"Quantifier elimination","score":0.4446895718574524},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4104650318622589},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12659063935279846},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.08210718631744385},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08077359199523926},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.05375584959983826}],"concepts":[{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.9212269186973572},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7031558752059937},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6771180033683777},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6624709367752075},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5843191146850586},{"id":"https://openalex.org/C2778523021","wikidata":"https://www.wikidata.org/wiki/Q5532504","display_name":"Quantifier (linguistics)","level":2,"score":0.5725892782211304},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.49900221824645996},{"id":"https://openalex.org/C32278780","wikidata":"https://www.wikidata.org/wiki/Q1849020","display_name":"Quantifier elimination","level":2,"score":0.4446895718574524},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4104650318622589},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12659063935279846},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.08210718631744385},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08077359199523926},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.05375584959983826},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2307/2272316","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2272316","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W40029885","https://openalex.org/W195189594","https://openalex.org/W848570700","https://openalex.org/W984419208","https://openalex.org/W1975943005","https://openalex.org/W1991402517","https://openalex.org/W2021757832","https://openalex.org/W2088529031","https://openalex.org/W4291439952","https://openalex.org/W4293117209"],"related_works":["https://openalex.org/W4214737172","https://openalex.org/W2069948376","https://openalex.org/W2102584526","https://openalex.org/W3012938552","https://openalex.org/W2324712051","https://openalex.org/W2798639752","https://openalex.org/W1524103539","https://openalex.org/W4287825236","https://openalex.org/W1239946963","https://openalex.org/W4243638815"],"abstract_inverted_index":{"Abstract":[0],"Let":[1],"\u2133":[2,58,84],"be":[3],"a":[4,7,11,42],"structure":[5],"for":[6,82],"language":[8],"\u2112":[9,54],"on":[10,103],"set":[12,21],"M":[13],"of":[14,34,57,70,77,95],"urelements.":[15],"HYP(\u2133)":[16],"is":[17,39],"the":[18,32,46,53,68,78],"least":[19],"admissible":[20,74],"above":[22],"\u2133.":[23],"In":[24,64],"\u00a71":[25],"we":[26,66],"show":[27,86],"that":[28,87],"pp":[29,80],"(HYP(\u2133))":[30,51,81],"[=":[31],"collection":[33],"pure":[35,72],"sets":[36,75,89],"in":[37,41],"HYP(\u2133)]":[38],"determined":[40],"simple":[43],"way":[44],"by":[45],"ordinal":[47],"\u03b1":[48,91],"=":[49],"\u00b0":[50],"and":[52,85,100],"x\u03c9":[55],"theory":[56],"up":[59],"to":[60],"quantifier":[61],"rank":[62],"\u03b1.":[63],"\u00a72":[65],"consider":[67],"question":[69,105],"which":[71],"countable":[73],"are":[76,94,106],"form":[79],"some":[83],"all":[88],"L":[90],"(\u03b1":[92],"admissible)":[93],"this":[96,104],"form.":[97],"Other":[98],"positive":[99],"negative":[101],"results":[102],"obtained.":[107]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
