{"id":"https://openalex.org/W2112129749","doi":"https://doi.org/10.2178/jsl/1185803630","title":"Assignment of ordinals to patterns of resemblance","display_name":"Assignment of ordinals to patterns of resemblance","publication_year":2007,"publication_date":"2007-06-01","ids":{"openalex":"https://openalex.org/W2112129749","doi":"https://doi.org/10.2178/jsl/1185803630","mag":"2112129749"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1185803630","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1185803630","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/A5019535832","display_name":"Gunnar Wilken","orcid":"https://orcid.org/0000-0002-4019-9320"},"institutions":[{"id":"https://openalex.org/I52357470","display_name":"The Ohio State University","ror":"https://ror.org/00rs6vg23","country_code":"US","type":"education","lineage":["https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Gunnar Wilken","raw_affiliation_strings":["Department of Mathematics, The Ohio State University, 130 Math Tower, 231 W 18th Avenue, Columbus, Ohio 43210, USA, E-mail:","Department of Mathematics, The Ohio State University, 130 Math Tower, 231 W 18th Avenue, Columbus, Ohio 43210, USA, E-mail: wilkeng@math.ohio-state.edu"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Ohio State University, 130 Math Tower, 231 W 18th Avenue, Columbus, Ohio 43210, USA, E-mail:","institution_ids":["https://openalex.org/I52357470"]},{"raw_affiliation_string":"Department of Mathematics, The Ohio State University, 130 Math Tower, 231 W 18th Avenue, Columbus, Ohio 43210, USA, E-mail: wilkeng@math.ohio-state.edu","institution_ids":["https://openalex.org/I52357470"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5019535832"],"corresponding_institution_ids":["https://openalex.org/I52357470"],"apc_list":null,"apc_paid":null,"fwci":0.3643,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.64815203,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"72","issue":"2","first_page":"704","last_page":"720"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9958000183105469,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9958000183105469,"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":0.932699978351593,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9284999966621399,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.7578014135360718},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.7244580984115601},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.7100924253463745},{"id":"https://openalex.org/keywords/arithmetic-function","display_name":"Arithmetic function","score":0.47474390268325806},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.4429360330104828},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.43271175026893616},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40847721695899963},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3479212820529938},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2975245714187622}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7578014135360718},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.7244580984115601},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.7100924253463745},{"id":"https://openalex.org/C112343008","wikidata":"https://www.wikidata.org/wiki/Q140744","display_name":"Arithmetic function","level":2,"score":0.47474390268325806},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.4429360330104828},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.43271175026893616},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40847721695899963},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3479212820529938},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2975245714187622},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2178/jsl/1185803630","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1185803630","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/1185803630","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1185803630","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":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1514633965","https://openalex.org/W2018457617","https://openalex.org/W2031449549","https://openalex.org/W2032474274","https://openalex.org/W2081882471","https://openalex.org/W2094980193","https://openalex.org/W3039529476","https://openalex.org/W4236380022"],"related_works":["https://openalex.org/W2087001086","https://openalex.org/W2065224863","https://openalex.org/W2078817350","https://openalex.org/W3011202710","https://openalex.org/W1982451148","https://openalex.org/W2908496801","https://openalex.org/W2155639834","https://openalex.org/W3182728725","https://openalex.org/W2112129749","https://openalex.org/W2076241292"],"abstract_inverted_index":{"Abstract":[0],"In":[1,72],"[2]":[2],"T.":[3],"J.":[4],"Carlson":[5],"introduces":[6],"an":[7,51,78],"approach":[8],"to":[9,120],"ordinal":[10,28,35,53,63,90],"notation":[11],"systems":[12],"which":[13,115],"is":[14,56],"based":[15,37,57],"on":[16,38,58,100],"the":[17,34,48,73,83,86,93,101,121],"notion":[18],"of":[19,33,50,61,89,103,106],"\u03a3":[20,39],"1":[21,40],"-elementary":[22],"substructure.":[23],"We":[24],"gave":[25],"a":[26,59,104],"detailed":[27],"arithmetical":[29],"analysis":[30],"(see":[31],"[7])":[32],"structure":[36],"-elementarily":[41],"as":[42],"defined":[43],"in":[44],"[2].":[45],"This":[46],"involved":[47],"development":[49],"appropriate":[52],"arithmetic":[54],"that":[55],"system":[60,88],"classical":[62,84],"notations":[64,91],"derived":[65],"from":[66,95],"Skolem":[67],"hull":[68],"operators,":[69],"see":[70],"[6].":[71],"present":[74],"paper":[75],"we":[76,108],"establish":[77],"effective":[79],"order":[80],"isomorphism":[81],"between":[82],"and":[85,97],"new":[87],"using":[92],"results":[94],"[6]":[96],"[7].":[98],"Moreover,":[99],"basis":[102],"concept":[105],"relativization":[107],"develop":[109],"mutual":[110],"(relatively)":[111],"elementary":[112],"recursive":[113],"assignments":[114],"are":[116],"uniform":[117],"with":[118],"respect":[119],"underlying":[122],"relativization.":[123]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
