{"id":"https://openalex.org/W2069073327","doi":"https://doi.org/10.1305/ndjfl/1093891806","title":"A note on ${\\cal P}$-admissible sets with urelements.","display_name":"A note on ${\\cal P}$-admissible sets with urelements.","publication_year":1975,"publication_date":"1975-07-01","ids":{"openalex":"https://openalex.org/W2069073327","doi":"https://doi.org/10.1305/ndjfl/1093891806","mag":"2069073327"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1093891806","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093891806","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-16/issue-3/A-note-on-cal-P-admissible-sets-with-urelements/10.1305/ndjfl/1093891806.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-16/issue-3/A-note-on-cal-P-admissible-sets-with-urelements/10.1305/ndjfl/1093891806.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004721342","display_name":"Judy Green","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Judy Green","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5004721342"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.22384368,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"16","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9864000082015991,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9864000082015991,"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/T12508","display_name":"Functional Equations Stability Results","score":0.9822999835014343,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.5460630655288696},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33884286880493164}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5460630655288696},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33884286880493164}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1305/ndjfl/1093891806","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093891806","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-16/issue-3/A-note-on-cal-P-admissible-sets-with-urelements/10.1305/ndjfl/1093891806.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.ndjfl/1093891806","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1093891806","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":{"id":"doi:10.1305/ndjfl/1093891806","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093891806","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-16/issue-3/A-note-on-cal-P-admissible-sets-with-urelements/10.1305/ndjfl/1093891806.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320333987","display_name":"Research Council, Rutgers, The State University of New Jersey","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2069073327.pdf","grobid_xml":"https://content.openalex.org/works/W2069073327.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W1125945453","https://openalex.org/W1991402517","https://openalex.org/W2131495252","https://openalex.org/W4234245490","https://openalex.org/W6627128721","https://openalex.org/W6648183425","https://openalex.org/W6679754079","https://openalex.org/W6815749489"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2042127053","https://openalex.org/W2142036596","https://openalex.org/W4238204885"],"abstract_inverted_index":{"In":[0],"[2]":[1,135],"Barwise":[2],"states":[3],"that":[4,33],"although":[5],"the":[6,19,37,57,87,90,97,110,121,132,146,163,209],"introduction":[7,17,35],"of":[8,40,56,89,112,126,134,153],"urelements":[9,54],"into":[10,18,36,193],"Zermelo-Fraenkel":[11],"set":[12,42,113,124,169],"theory":[13,22,39,91],"is":[14,26,45,73,102],"redundant,":[15],"their":[16,34],"weaker":[20],"Kripke-Platek":[21],"for":[23,145,162],"admissible":[24,43],"sets":[25,44,52],"not.In":[27],"this":[28],"note*":[29],"we":[30],"will":[31],"show":[32],"intermediate":[38],"power":[41],"once":[46],"again":[47],"redundant":[48],"since":[49],"all":[50],"/'-admissible":[51],"with":[53,86,94,109],"are":[55],"same":[58],"form":[59],"as":[60,136],"/^-admissible":[61],"sets,":[62],"i.e.,":[63],"V":[64],"M":[65,66,69],"=":[67,80,158],"H":[68],"(/<)":[70],"where":[71],"K":[72,79,82],"a":[74,155,167,175,188],"strong":[75],"limit":[76],"cardinal":[77],"and":[78,96,120,128,198,203],"3":[81],".We":[83],"assume":[84,107],"familiarity":[85,108],"formulation":[88],"KPU":[92],"(Kripke-Platek":[93],"urelements>":[95],"language":[98,147,164],"in":[99,212],"which":[100,207],"it":[101],"formulated":[103],"(see":[104],"[2]).We":[105],"also":[106],"hierarchy":[111],"theoretic":[114],"predicates":[115],"due":[116],"to":[117,184,195],"Levy":[118],"[5],":[119],"primitive":[122],"recursive":[123],"functions":[125],"Jensen":[127],"Karp":[129],"[4].We":[130],"expand":[131],"notation":[133],"follows:Definition:":[137],"A":[138,170,183,192,194],"structure":[139,156],"Sl^":[140],"(9W;":[141],"A,":[142],"E,":[143],"P,...)":[144],"L(e,":[148,213],"P,":[149,197,214],".":[150,160,215],"..)":[151,161],"consists":[152],"(1)":[154],"9J\u03aa":[157],"(M,":[159],"L,":[165],"(2)":[166],"nonempty":[168],"disjoint":[171],"from":[172,191],"M,":[173],"(3)":[174],"relation":[176],"E":[177],"c":[178],"(M":[179],"U":[180],"A)":[181],"x":[182],"interpret":[185,196,208],"e,":[186],"(4)":[187],"function":[189],"P":[190],"(5)":[199],"other":[200,210],"functions,":[201],"relations,":[202],"constants":[204],"on":[205],"MUA":[206],"symbols":[211],"..).":[216]},"counts_by_year":[],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}
