{"id":"https://openalex.org/W1996225872","doi":"https://doi.org/10.1002/malq.19930390106","title":"A variant of the Notion of Semicreative set","display_name":"A variant of the Notion of Semicreative set","publication_year":1993,"publication_date":"1993-01-01","ids":{"openalex":"https://openalex.org/W1996225872","doi":"https://doi.org/10.1002/malq.19930390106","mag":"1996225872"},"language":"en","primary_location":{"id":"doi:10.1002/malq.19930390106","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19930390106","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["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/A5085012955","display_name":"Heinrich Rolletschek","orcid":null},"institutions":[{"id":"https://openalex.org/I121883995","display_name":"Johannes Kepler University of Linz","ror":"https://ror.org/052r2xn60","country_code":"AT","type":"education","lineage":["https://openalex.org/I121883995"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Heinrich Rolletschek","raw_affiliation_strings":["Research Institute for Symbolic Computation, Johannes Kepler Universita\u0308t 4040 \u2014 Linz, Austria","Research Institute for Symbolic Computation, Johannes Kepler Universit\u00e4t 4040 \u2014 Linz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Research Institute for Symbolic Computation, Johannes Kepler Universita\u0308t 4040 \u2014 Linz, Austria","institution_ids":["https://openalex.org/I121883995"]},{"raw_affiliation_string":"Research Institute for Symbolic Computation, Johannes Kepler Universit\u00e4t 4040 \u2014 Linz, Austria","institution_ids":["https://openalex.org/I121883995"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5085012955"],"corresponding_institution_ids":["https://openalex.org/I121883995"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14856255,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"39","issue":"1","first_page":"33","last_page":"46"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11079","display_name":"Creativity in Education and Neuroscience","score":0.9642999768257141,"subfield":{"id":"https://openalex.org/subfields/3205","display_name":"Experimental and Cognitive Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11079","display_name":"Creativity in Education and Neuroscience","score":0.9642999768257141,"subfield":{"id":"https://openalex.org/subfields/3205","display_name":"Experimental and Cognitive Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9132999777793884,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9046000242233276,"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/counterexample","display_name":"Counterexample","score":0.8945293426513672},{"id":"https://openalex.org/keywords/dedekind-cut","display_name":"Dedekind cut","score":0.7308188676834106},{"id":"https://openalex.org/keywords/creativity","display_name":"Creativity","score":0.715012788772583},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7038350105285645},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6778308749198914},{"id":"https://openalex.org/keywords/join","display_name":"Join (topology)","score":0.44959843158721924},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3286169767379761},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3084326982498169},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20012393593788147},{"id":"https://openalex.org/keywords/social-psychology","display_name":"Social psychology","score":0.09422463178634644},{"id":"https://openalex.org/keywords/psychology","display_name":"Psychology","score":0.08100107312202454},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.06312906742095947}],"concepts":[{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.8945293426513672},{"id":"https://openalex.org/C76449584","wikidata":"https://www.wikidata.org/wiki/Q851333","display_name":"Dedekind cut","level":2,"score":0.7308188676834106},{"id":"https://openalex.org/C11012388","wikidata":"https://www.wikidata.org/wiki/Q170658","display_name":"Creativity","level":2,"score":0.715012788772583},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7038350105285645},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6778308749198914},{"id":"https://openalex.org/C2776124973","wikidata":"https://www.wikidata.org/wiki/Q3183033","display_name":"Join (topology)","level":2,"score":0.44959843158721924},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3286169767379761},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3084326982498169},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20012393593788147},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.09422463178634644},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.08100107312202454},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.06312906742095947}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/malq.19930390106","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19930390106","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W2008273724","https://openalex.org/W2053099695","https://openalex.org/W2056414301","https://openalex.org/W2062249564","https://openalex.org/W2070390550","https://openalex.org/W2077783082","https://openalex.org/W2530006810","https://openalex.org/W2905135108","https://openalex.org/W4232277851","https://openalex.org/W4235794029","https://openalex.org/W4235948263","https://openalex.org/W4255479900"],"related_works":["https://openalex.org/W4387497383","https://openalex.org/W3183948672","https://openalex.org/W3173606202","https://openalex.org/W3110381201","https://openalex.org/W2948807893","https://openalex.org/W2935909890","https://openalex.org/W2778153218","https://openalex.org/W2758277628","https://openalex.org/W2748952813","https://openalex.org/W1531601525"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"paper":[2],"introduces":[3],"the":[4,50,71,89],"notion":[5],"of":[6,12,29,52,73],"cW10\u2010creative":[7],"set,":[8],"which":[9,30,104],"strengthens":[10,22],"that":[11,32,43,64],"semicreative":[13,35,44,53],"set":[14],"in":[15],"a":[16,106],"similar":[17],"way":[18],"as":[19],"complete":[20],"creativity":[21],"creativity.":[23],"Two":[24],"results":[25],"are":[26,37],"proven,":[27],"both":[28],"imply":[31],"not":[33,92],"all":[34],"sets":[36,100],"cW10\u2010creative.":[38],"First,":[39],"it":[40,61],"is":[41,62,78,85,91],"shown":[42,57,63],"Dedekind":[45,54],"cuts":[46,55],"cannot":[47],"be":[48,111],"cW10\u2010creative;":[49],"existence":[51],"was":[56],"by":[58,97],"Soare.":[59],"Secondly,":[60],"(i)":[65],"if":[66],"A":[67,74,82,101],"\u2295":[68],"B":[69,76,84,103],",":[70,77,102],"join":[72],"and":[75,87],"cW10\u2010creative,":[79,86],"then":[80],"either":[81],"or":[83],"(ii)":[88,109],"same":[90],"true":[93],"with":[94],"\u2018cW10\u2010creative\u2019":[95],"replaced":[96],"\u2018semicreative\u2019.":[98],"Moreover,":[99],"provide":[105],"counterexample":[107],"for":[108],"can":[110],"constructed":[112],"within":[113],"any":[114],"given":[115],"nonrecursive":[116],"r.e.":[117],"T\u2010degrees":[118],"a,":[119],"b.":[120],"MSC:":[121],"03D30.":[122]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}