{"id":"https://openalex.org/W4391138310","doi":"https://doi.org/10.1007/s11083-024-09658-w","title":"Higman\u2019s Lemma is Stronger for Better Quasi Orders","display_name":"Higman\u2019s Lemma is Stronger for Better Quasi Orders","publication_year":2024,"publication_date":"2024-01-23","ids":{"openalex":"https://openalex.org/W4391138310","doi":"https://doi.org/10.1007/s11083-024-09658-w"},"language":"en","primary_location":{"id":"doi:10.1007/s11083-024-09658-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11083-024-09658-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11083-024-09658-w.pdf","source":{"id":"https://openalex.org/S121371512","display_name":"Order","issn_l":"0167-8094","issn":["0167-8094","1572-9273"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Order","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11083-024-09658-w.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071872554","display_name":"Anton Freund","orcid":"https://orcid.org/0000-0002-5456-5790"},"institutions":[{"id":"https://openalex.org/I25974101","display_name":"University of W\u00fcrzburg","ror":"https://ror.org/00fbnyb24","country_code":"DE","type":"education","lineage":["https://openalex.org/I25974101"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Anton Freund","raw_affiliation_strings":["Institute of Mathematics, University of W\u00fcrzburg, Emil-Fischer-Str.\u00a040, 97074, W\u00fcrzburg, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of W\u00fcrzburg, Emil-Fischer-Str.\u00a040, 97074, W\u00fcrzburg, Germany","institution_ids":["https://openalex.org/I25974101"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5071872554"],"corresponding_institution_ids":["https://openalex.org/I25974101"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01434827,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"41","issue":"3","first_page":"753","last_page":"759"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998999834060669,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998999834060669,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9991000294685364,"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"}},{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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":0.8445934057235718},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.7886313199996948},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5746104121208191},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38420116901397705},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34150296449661255},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28741276264190674}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8445934057235718},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.7886313199996948},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5746104121208191},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38420116901397705},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34150296449661255},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28741276264190674},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s11083-024-09658-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11083-024-09658-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11083-024-09658-w.pdf","source":{"id":"https://openalex.org/S121371512","display_name":"Order","issn_l":"0167-8094","issn":["0167-8094","1572-9273"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Order","raw_type":"journal-article"},{"id":"pmh:oai:opus.bibliothek.uni-wuerzburg.de:39856","is_oa":true,"landing_page_url":"https://nbn-resolving.org/urn:nbn:de:bvb:20-opus-398565","pdf_url":"https://opus.bibliothek.uni-wuerzburg.de/files/39856/11083_2024_Article_9658.pdf","source":{"id":"https://openalex.org/S4306401635","display_name":"Online Publication Service of W\u00fcrzburg University (W\u00fcrzburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I25974101","host_organization_name":"University of W\u00fcrzburg","host_organization_lineage":["https://openalex.org/I25974101"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"doc-type:article"}],"best_oa_location":{"id":"doi:10.1007/s11083-024-09658-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11083-024-09658-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11083-024-09658-w.pdf","source":{"id":"https://openalex.org/S121371512","display_name":"Order","issn_l":"0167-8094","issn":["0167-8094","1572-9273"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Order","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3852438965","display_name":null,"funder_award_id":"460597863","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5106512922","display_name":null,"funder_award_id":"Deutsche Forschungsgemeinschaft (DFG","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320325356","display_name":"Julius-Maximilians-Universit\u00e4t W\u00fcrzburg","ror":"https://ror.org/00fbnyb24"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4391138310.pdf"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W178720230","https://openalex.org/W2076508310","https://openalex.org/W2104452294","https://openalex.org/W2131443763","https://openalex.org/W2134705851","https://openalex.org/W2138899395","https://openalex.org/W2143608087","https://openalex.org/W2146064316","https://openalex.org/W2170311001","https://openalex.org/W2218992691","https://openalex.org/W2963030916","https://openalex.org/W3106208063","https://openalex.org/W4229690001","https://openalex.org/W4232407185","https://openalex.org/W4367055849"],"related_works":["https://openalex.org/W3006682748","https://openalex.org/W1979597421","https://openalex.org/W1097487277","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2768610039","https://openalex.org/W2735923117","https://openalex.org/W2115913661","https://openalex.org/W3168772390"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"prove":[2],"that":[3,45],"Higman\u2019s":[4],"lemma":[5],"is":[6,40,94],"strictly":[7],"stronger":[8,29],"for":[9,14,77],"better":[10],"quasi":[11,16],"orders":[12],"than":[13],"well":[15,79],"orders,":[17],"within":[18],"the":[19,31,43,97],"framework":[20],"of":[21,37],"reverse":[22],"mathematics.":[23],"In":[24],"fact,":[25],"we":[26],"show":[27],"a":[28,78],"result:":[30],"infinite":[32],"Ramsey":[33],"theorem":[34],"(for":[35],"tuples":[36],"all":[38],"lengths)":[39],"equivalent":[41],"to":[42],"statement":[44],"any":[46],"array":[47],"$$[\\mathbb":[48],"N]^{n+1}\\rightarrow":[49],"\\mathbb":[50,84],"N^n\\times":[51],"X$$":[52],"<mml:math":[53,86,102],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[54,87,103],"<mml:mrow>":[55,57,62,88],"<mml:msup>":[56,69],"<mml:mo>[</mml:mo>":[58],"<mml:mi>N</mml:mi>":[59,70,91],"<mml:mo>]</mml:mo>":[60],"</mml:mrow>":[61,66,75,92],"<mml:mi>n</mml:mi>":[63,71,89],"<mml:mo>+</mml:mo>":[64],"<mml:mn>1</mml:mn>":[65],"</mml:msup>":[67,72],"<mml:mo>\u2192</mml:mo>":[68],"<mml:mo>\u00d7</mml:mo>":[73],"<mml:mi>X</mml:mi>":[74],"</mml:math>":[76,93,108],"order":[80],"X":[81],"and":[82],"$$n\\in":[83],"N$$":[85],"<mml:mo>\u2208</mml:mo>":[90],"good,":[95],"over":[96],"base":[98],"theory":[99],"$$\\mathsf":[100],"{RCA_0}$$":[101],"<mml:msub>":[104],"<mml:mi>RCA</mml:mi>":[105],"<mml:mn>0</mml:mn>":[106],"</mml:msub>":[107],".":[109]},"counts_by_year":[],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
