{"id":"https://openalex.org/W1975528681","doi":"https://doi.org/10.1002/malq.200410028","title":"The complexity of plane hyperbolic incidence geometry is ????","display_name":"The complexity of plane hyperbolic incidence geometry is ????","publication_year":2005,"publication_date":"2005-03-18","ids":{"openalex":"https://openalex.org/W1975528681","doi":"https://doi.org/10.1002/malq.200410028","mag":"1975528681"},"language":"en","primary_location":{"id":"doi:10.1002/malq.200410028","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.200410028","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":"MLQ","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/A5038599115","display_name":"Victor Pambuccian","orcid":"https://orcid.org/0000-0003-2263-1471"},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Victor Pambuccian","raw_affiliation_strings":["Department of Integrative Studies, Arizona State University \u2013 West Campus, P. O. Box 37100, Phoenix AZ 85069-7100, USA","Department of Integrative Studies, Arizona State University \u2013 West Campus, P. O. Box 37100, Phoenix AZ 85069\u20107100, USA"],"affiliations":[{"raw_affiliation_string":"Department of Integrative Studies, Arizona State University \u2013 West Campus, P. O. Box 37100, Phoenix AZ 85069-7100, USA","institution_ids":["https://openalex.org/I55732556"]},{"raw_affiliation_string":"Department of Integrative Studies, Arizona State University \u2013 West Campus, P. O. Box 37100, Phoenix AZ 85069\u20107100, USA","institution_ids":["https://openalex.org/I55732556"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5038599115"],"corresponding_institution_ids":["https://openalex.org/I55732556"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":2.1345,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.85273541,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"51","issue":"3","first_page":"277","last_page":"281"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9995999932289124,"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/T12170","display_name":"History and Theory of Mathematics","score":0.9818000197410583,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9746000170707703,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.8068527579307556},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7902830839157104},{"id":"https://openalex.org/keywords/collinearity","display_name":"Collinearity","score":0.6589918732643127},{"id":"https://openalex.org/keywords/hyperbolic-triangle","display_name":"Hyperbolic triangle","score":0.6272178888320923},{"id":"https://openalex.org/keywords/hyperbolic-geometry","display_name":"Hyperbolic geometry","score":0.5724821090698242},{"id":"https://openalex.org/keywords/foundations-of-geometry","display_name":"Foundations of geometry","score":0.5604937076568604},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5524383187294006},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.5171474814414978},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4934362471103668},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4538399875164032},{"id":"https://openalex.org/keywords/projective-geometry","display_name":"Projective geometry","score":0.1586816906929016},{"id":"https://openalex.org/keywords/differential-geometry","display_name":"Differential geometry","score":0.1572442352771759}],"concepts":[{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.8068527579307556},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7902830839157104},{"id":"https://openalex.org/C106192678","wikidata":"https://www.wikidata.org/wiki/Q1419761","display_name":"Collinearity","level":2,"score":0.6589918732643127},{"id":"https://openalex.org/C82673646","wikidata":"https://www.wikidata.org/wiki/Q2246553","display_name":"Hyperbolic triangle","level":4,"score":0.6272178888320923},{"id":"https://openalex.org/C206352148","wikidata":"https://www.wikidata.org/wiki/Q209306","display_name":"Hyperbolic geometry","level":3,"score":0.5724821090698242},{"id":"https://openalex.org/C180110497","wikidata":"https://www.wikidata.org/wiki/Q5474574","display_name":"Foundations of geometry","level":4,"score":0.5604937076568604},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5524383187294006},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.5171474814414978},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4934362471103668},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4538399875164032},{"id":"https://openalex.org/C185362025","wikidata":"https://www.wikidata.org/wiki/Q177409","display_name":"Projective geometry","level":3,"score":0.1586816906929016},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.1572442352771759},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/malq.200410028","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.200410028","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":"MLQ","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322957","display_name":"Westf\u00e4lische Wilhelms-Universit\u00e4t M\u00fcnster","ror":"https://ror.org/00pd74e08"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W188101875","https://openalex.org/W1969611119","https://openalex.org/W1982232476","https://openalex.org/W1998607986","https://openalex.org/W2046731118","https://openalex.org/W6626177386","https://openalex.org/W6626778872"],"related_works":["https://openalex.org/W4230858366","https://openalex.org/W3149012514","https://openalex.org/W4243116182","https://openalex.org/W136616785","https://openalex.org/W4300116253","https://openalex.org/W2034320749","https://openalex.org/W1871288014","https://openalex.org/W3216145041","https://openalex.org/W4365934646","https://openalex.org/W1005121375"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2,31],"plane":[3],"hyperbolic":[4,50],"geometry,":[5],"expressed":[6,20],"in":[7],"terms":[8],"of":[9,15,23,25,38],"points":[10],"and":[11],"the":[12],"ternary":[13],"relation":[14],"collinearity":[16],"alone,":[17],"cannot":[18],"be":[19],"by":[21],"means":[22],"axioms":[24,40],"complexity":[26],"at":[27],"most":[28],"\u2200\u2203\u2200,":[29],"but":[30],"there":[32],"is":[33],"an":[34],"axiom":[35],"system,":[36],"all":[37],"whose":[39],"are":[41],"\u2200\u2203\u2200\u2203":[42],"sentences.":[43],"This":[44],"remains":[45],"true":[46],"for":[47],"Klingenberg's":[48],"generalized":[49],"planes,":[51],"with":[52],"arbitrary":[53],"ordered":[54],"fields":[55],"as":[56],"coordinate":[57],"fields.":[58],"(\u00a9":[59],"2005":[60],"WILEY-VCH":[61],"Verlag":[62],"GmbH":[63],"&":[64],"Co.":[65],"KGaA,":[66],"Weinheim)":[67]},"counts_by_year":[{"year":2021,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}