{"id":"https://openalex.org/W4255405682","doi":"https://doi.org/10.1305/ndjfl/1093634488","title":"Counting functions.","display_name":"Counting functions.","publication_year":1992,"publication_date":"1992-09-01","ids":{"openalex":"https://openalex.org/W4255405682","doi":"https://doi.org/10.1305/ndjfl/1093634488"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1093634488","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093634488","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-33/issue-4/Counting-functions/10.1305/ndjfl/1093634488.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-33/issue-4/Counting-functions/10.1305/ndjfl/1093634488.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052601669","display_name":"Fred A. Johnson","orcid":"https://orcid.org/0000-0002-5854-3695"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Fred Johnson","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5052601669"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.43601616,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"33","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.3176000118255615,"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"}},"topics":[{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.3176000118255615,"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/mathematics","display_name":"Mathematics","score":0.3928731083869934},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3817369043827057}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3928731083869934},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3817369043827057}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1305/ndjfl/1093634488","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093634488","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-33/issue-4/Counting-functions/10.1305/ndjfl/1093634488.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/1093634488","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1093634488","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:mountainscholar.org:10217/198387","is_oa":false,"landing_page_url":"https://hdl.handle.net/10217/198387","pdf_url":null,"source":{"id":"https://openalex.org/S4306402292","display_name":"Digital Collections of Colorado (Colorado State University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I92446798","host_organization_name":"Colorado State University","host_organization_lineage":["https://openalex.org/I92446798"],"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/1093634488","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093634488","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-33/issue-4/Counting-functions/10.1305/ndjfl/1093634488.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/F4320309627","display_name":"Colorado State University","ror":"https://ror.org/03k1gpj17"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4255405682.pdf","grobid_xml":"https://content.openalex.org/works/W4255405682.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644"],"abstract_inverted_index":{"Counting":[0],"functions":[1,31],"are":[2,32],"shown":[3],"to":[4,41],"be":[5,81],"closed":[6,33],"under":[7,34],"composition.The":[8,35],"proof":[9,45],"by":[10],"Pelletier":[11],"and":[12,119,134],"Martin":[13],"[1]":[14],"of":[15,37,46,58,61,64,66,76,84,110],"Post's":[16],"Functional":[17],"Completeness":[18],"Theorem":[19],"contains":[20],"a":[21,43],"very":[22],"complex":[23],"argument":[24],"that":[25,29,113],"shows":[26],"in":[27,118,121],"effect":[28],"counting":[30,127],"purpose":[36],"this":[38,47],"note":[39],"is":[40,50,95,107,126,129],"give":[42],"simple":[44],"result.A":[48],"function/\"":[49,125],"an":[51,82,96,108,130],"n-ary":[52,131],"truth":[53,67,85,111,132],"function":[54,133],"iff":[55],"the":[56,62,77,122],"domain":[57],"/\"":[59],"consists":[60],"set":[63],"^-tuples":[65],"values":[68,112],"(/":[69],"and/)":[70],"and/\"":[71],"assigns":[72],"torfto":[73],"each":[74],"member":[75],"domain.Let":[78],"R":[79,101,105,116,139,151,155],"n":[80,87,106,117],"/2-tuple":[83],"values.O":[86],"j,":[88],"for":[89,99,135],"1":[90],"<":[91,93],"i":[92],"n,":[94],"operator":[97],"iff,":[98],"every":[100,136,138,154],"n9":[102],"O":[103],"ni":[104],"w-tuple":[109],"differs":[114],"from":[115],"only":[120],"/th":[123],"place.A":[124],"iff/\"":[128],"operatorfor":[137],"2":[140,142,144,148,152,156],"and/":[141],"(\u039b":[143],")":[145],"\u03a6":[146],"f":[147],"(O":[149],"2>2":[150],")for":[153],".)":[157]},"counts_by_year":[],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2022-05-12T00:00:00"}
