{"id":"https://openalex.org/W1992475229","doi":"https://doi.org/10.1002/malq.19950410102","title":"Existentially Complete Nerode Semirings","display_name":"Existentially Complete Nerode Semirings","publication_year":1995,"publication_date":"1995-01-01","ids":{"openalex":"https://openalex.org/W1992475229","doi":"https://doi.org/10.1002/malq.19950410102","mag":"1992475229"},"language":"en","primary_location":{"id":"doi:10.1002/malq.19950410102","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19950410102","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/A5109841134","display_name":"T. G. McLaughlin","orcid":null},"institutions":[{"id":"https://openalex.org/I12315562","display_name":"Texas Tech University","ror":"https://ror.org/0405mnx93","country_code":"US","type":"education","lineage":["https://openalex.org/I12315562"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Thomas G. McLaughlin","raw_affiliation_strings":["Department of Mathematics, Texas Tech University, Lubbock, Texas 79409, U.S.A","Department of Mathematics Texas Tech University, Lubbock, Texas 79409, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Texas Tech University, Lubbock, Texas 79409, U.S.A","institution_ids":["https://openalex.org/I12315562"]},{"raw_affiliation_string":"Department of Mathematics Texas Tech University, Lubbock, Texas 79409, U.S.A","institution_ids":["https://openalex.org/I12315562"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5109841134"],"corresponding_institution_ids":["https://openalex.org/I12315562"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.10856577,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"41","issue":"1","first_page":"1","last_page":"14"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9890000224113464,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9890000224113464,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9872000217437744,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9771999716758728,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/semiring","display_name":"Semiring","score":0.805024266242981},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.775202751159668},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.6059814095497131},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.5392791628837585},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.5016427040100098},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.5008425712585449},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.4518643021583557},{"id":"https://openalex.org/keywords/partial-function","display_name":"Partial function","score":0.4454949200153351},{"id":"https://openalex.org/keywords/kleene-algebra","display_name":"Kleene algebra","score":0.42619985342025757},{"id":"https://openalex.org/keywords/partially-ordered-set","display_name":"Partially ordered set","score":0.4124471843242645},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3989489674568176},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.34546661376953125},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34512531757354736}],"concepts":[{"id":"https://openalex.org/C21696900","wikidata":"https://www.wikidata.org/wiki/Q1333055","display_name":"Semiring","level":2,"score":0.805024266242981},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.775202751159668},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.6059814095497131},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.5392791628837585},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.5016427040100098},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.5008425712585449},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.4518643021583557},{"id":"https://openalex.org/C182359184","wikidata":"https://www.wikidata.org/wiki/Q1756942","display_name":"Partial function","level":2,"score":0.4454949200153351},{"id":"https://openalex.org/C206470798","wikidata":"https://www.wikidata.org/wiki/Q2634506","display_name":"Kleene algebra","level":2,"score":0.42619985342025757},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.4124471843242645},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3989489674568176},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34546661376953125},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34512531757354736},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/malq.19950410102","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19950410102","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":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.5799999833106995}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W658415929","https://openalex.org/W1484200610","https://openalex.org/W1964837558","https://openalex.org/W1965339341","https://openalex.org/W1995881727","https://openalex.org/W2033165530","https://openalex.org/W2047724249","https://openalex.org/W2061991358","https://openalex.org/W2068573065","https://openalex.org/W2096478770","https://openalex.org/W2142676041","https://openalex.org/W2313398169","https://openalex.org/W2320814124","https://openalex.org/W4253337930"],"related_works":["https://openalex.org/W2033560440","https://openalex.org/W2741025110","https://openalex.org/W1540341981","https://openalex.org/W187758485","https://openalex.org/W1985776806","https://openalex.org/W2127942730","https://openalex.org/W3040795817","https://openalex.org/W4232125628","https://openalex.org/W2100036411","https://openalex.org/W2186303141"],"abstract_inverted_index":{"Abstract":[0],"Let":[1],"\u039b":[2,69],"denote":[3],"the":[4,37,43,66,71,76,106,133,141],"semiring":[5],"of":[6,15,19,65,70,75,82,86,109,135,143,148],"isols.":[7],"We":[8],"characterize":[9],"existential":[10,114],"completeness":[11,115],"for":[12,119,132],"Nerode":[13,40,122],"subsemirings":[14],"\u039b,":[16],"by":[17,92,99,111,124],"means":[18],"a":[20,83,120,127,158],"purely":[21,55],"isol\u2010theoretic":[22,56],"\u201c\u03a3":[23],"1":[24,50,73],"separation":[25],"property\u201d.":[26],"(A":[27],"\u201cconcrete\u201d":[28],"characterization":[29,53],"that":[30,45,58,113],"is":[31,34,54,60,80,116],"not":[32,117],"\u039b\u2010theoretic":[33],"well":[35],"known:":[36],"existentially":[38],"complete":[39],"semirings":[41],"are":[42,46,156],"ones":[44],"isomorphic":[47],"to":[48,68,90,97],"\u03a3":[49,72],"ultrapowers.)":[51],"Our":[52],"in":[57,63],"it":[59],"formulated":[61],"entirely":[62],"terms":[64],"extensions":[67,134],"subsets":[74],"natural":[77],"numbers.":[78],"Advantage":[79],"taken":[81],"special":[84],"kind":[85],"isol":[87],"first":[88,95],"conjectured":[89],"exist":[91,98],"Ellentuck":[93],"and":[94],"proven":[96],"Barback":[100],"(unpublished).":[101],"In":[102],"addition,":[103],"we":[104],"strengthen":[105],"negative":[107],"part":[108],"[13]":[110],"showing":[112],"secured,":[118],"given":[121],"semiring,":[123],"either":[125],"(i)":[126],"certain":[128],"\u201cfunctional":[129],"closure\u201d":[130],"property":[131,142],"partial":[136,150],"recursive":[137,151],"functions":[138],"or":[139],"(ii)":[140],"\u201cpulling":[144],"in\u201d":[145],"some":[146],"portion":[147],"each":[149],"fiber;":[152],"these":[153],"latter":[154],"results":[155],"perhaps":[157],"little":[159],"surprising.":[160]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
