{"id":"https://openalex.org/W2802849415","doi":"https://doi.org/10.1002/malq.201600020","title":"Normal forms, linearity, and prime algebraicity over nonflat domains","display_name":"Normal forms, linearity, and prime algebraicity over nonflat domains","publication_year":2018,"publication_date":"2018-04-01","ids":{"openalex":"https://openalex.org/W2802849415","doi":"https://doi.org/10.1002/malq.201600020","mag":"2802849415"},"language":"en","primary_location":{"id":"doi:10.1002/malq.201600020","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.201600020","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","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/A5029473922","display_name":"Basil A. Kar\u00e1dais","orcid":null},"institutions":[{"id":"https://openalex.org/I8204097","display_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/05591te55","country_code":"DE","type":"education","lineage":["https://openalex.org/I8204097"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Basil A. Kar\u00e1dais","raw_affiliation_strings":["Mathematisches Institut Ludwig\u2010Maximilians\u2010Universit\u00e4t Theresienstra\u00dfe 39 80333 M\u00fcnchen Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematisches Institut Ludwig\u2010Maximilians\u2010Universit\u00e4t Theresienstra\u00dfe 39 80333 M\u00fcnchen Germany","institution_ids":["https://openalex.org/I8204097"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5029473922"],"corresponding_institution_ids":["https://openalex.org/I8204097"],"apc_list":{"value":2900,"currency":"USD","value_usd":2900},"apc_paid":null,"fwci":0.1853,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.63008511,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"64","issue":"1-2","first_page":"55","last_page":"88"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9998999834060669,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.996399998664856,"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"}},{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9933000206947327,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7102581262588501},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.6703164577484131},{"id":"https://openalex.org/keywords/linear-logic","display_name":"Linear logic","score":0.6422368288040161},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5690326690673828},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5109857320785522},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.4731912612915039},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.44571495056152344},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4393959045410156},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.4215690493583679},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3284377157688141},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.28466182947158813},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2712060809135437}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7102581262588501},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.6703164577484131},{"id":"https://openalex.org/C28077239","wikidata":"https://www.wikidata.org/wiki/Q841728","display_name":"Linear logic","level":2,"score":0.6422368288040161},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5690326690673828},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5109857320785522},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.4731912612915039},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.44571495056152344},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4393959045410156},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.4215690493583679},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3284377157688141},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.28466182947158813},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2712060809135437},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/malq.201600020","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.201600020","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","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":30,"referenced_works":["https://openalex.org/W128738456","https://openalex.org/W171834292","https://openalex.org/W1487875360","https://openalex.org/W1508956995","https://openalex.org/W1544564247","https://openalex.org/W1547926009","https://openalex.org/W1668029505","https://openalex.org/W1719974439","https://openalex.org/W1966478469","https://openalex.org/W1977580460","https://openalex.org/W1991052229","https://openalex.org/W2007270285","https://openalex.org/W2039112578","https://openalex.org/W2072497723","https://openalex.org/W2082152502","https://openalex.org/W2093209788","https://openalex.org/W2109184180","https://openalex.org/W2122859326","https://openalex.org/W2133084975","https://openalex.org/W2134326845","https://openalex.org/W2144130305","https://openalex.org/W2346559250","https://openalex.org/W2913583188","https://openalex.org/W2949679094","https://openalex.org/W3146832245","https://openalex.org/W4205623740","https://openalex.org/W4213136552","https://openalex.org/W4233702006","https://openalex.org/W4250859358","https://openalex.org/W4301945969"],"related_works":["https://openalex.org/W3044435432","https://openalex.org/W2093595243","https://openalex.org/W2774637633","https://openalex.org/W2185671459","https://openalex.org/W2404664685","https://openalex.org/W4311225851","https://openalex.org/W2349865494","https://openalex.org/W3217635579","https://openalex.org/W2996573386","https://openalex.org/W2802849415"],"abstract_inverted_index":{"Abstract":[0],"Using":[1],"representations":[2,75],"of":[3,25,31,51,57,154,174,177],"nonflat":[4,69],"Scott":[5],"domains":[6],"to":[7,14,36,49,65,113,139,161,183],"model":[8,143],"type":[9,80],"systems,":[10],"it":[11,95],"is":[12],"natural":[13],"wish":[15],"that":[16,90,120,134,179],"they":[17],"be":[18,181],"\u201clinear\u201d,":[19],"in":[20,54,87,125,147],"which":[21],"case":[22],"the":[23,26,38,55,103,130,152,155],"complexity":[24],"fundamental":[27],"test":[28],"for":[29,76],"entailment":[30],"information":[32],"drops":[33],"from":[34],"exponential":[35],"linear,":[37],"corresponding":[39],"mathematical":[40],"theory":[41],"becomes":[42],"much":[43],"simpler,":[44],"and":[45,60,99,133,157,188],"moreover":[46],"has":[47],"ties":[48],"models":[50],"computation":[52],"arising":[53],"study":[56,172],"sequentiality,":[58],"concurrency,":[59],"linear":[61,73,142,189],"logic.":[62],"Earlier":[63],"attempts":[64],"develop":[66],"a":[67,77,88,126,140,148,163],"fully":[68,141],"semantics":[70],"based":[71],"on":[72,106],"domain":[74],"rich":[78],"enough":[79],"system":[81],"allowing":[82],"inductive":[83],"types,":[84],"were":[85],"designed":[86],"way":[89,128],"felt":[91],"rather":[92],"artificial,":[93],"as":[94],"featured":[96],"certain":[97],"awkward":[98],"counter\u2010intuitive":[100],"properties;":[101],"eventually,":[102],"focus":[104],"turned":[105],"general,":[107],"nonlinear":[108,131,156],"representations.":[109],"Here":[110],"we":[111,121,135,171],"try":[112],"turn":[114,184],"this":[115],"situation":[116],"around,":[117],"by":[118],"showing":[119],"can":[122,180],"work":[123],"linearly":[124],"systematic":[127],"within":[129],"model,":[132],"may":[136],"even":[137],"restrict":[138],"whose":[144],"objects":[145,178],"are":[146,158],"bijective":[149],"correspondence":[150],"with":[151],"ones":[153],"easily":[159],"seen":[160],"form":[162],"prime":[164],"algebraic":[165],"domain.":[166],"To":[167],"obtain":[168],"our":[169],"results":[170],"mappings":[173],"finite":[175],"approximations":[176,185],"used":[182],"into":[186],"normal":[187],"forms.":[190]},"counts_by_year":[{"year":2018,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}