{"id":"https://openalex.org/W2091601619","doi":"https://doi.org/10.2178/jsl/1190150113","title":"More undecidable lattices of Steinitz exchange systems","display_name":"More undecidable lattices of Steinitz exchange systems","publication_year":2002,"publication_date":"2002-06-01","ids":{"openalex":"https://openalex.org/W2091601619","doi":"https://doi.org/10.2178/jsl/1190150113","mag":"2091601619"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1190150113","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1190150113","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/A5089817196","display_name":"Lisa Galminas","orcid":null},"institutions":[{"id":"https://openalex.org/I157717896","display_name":"Northwestern State University","ror":"https://ror.org/049ams583","country_code":"US","type":"education","lineage":["https://openalex.org/I157717896","https://openalex.org/I2799628689"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"L. R. Galminas","raw_affiliation_strings":["Department of Mathematics, Northwestern State University of Louisiana, Natchitoches, LA 71457., USA, E-mail:","Department of Mathematics, Northwestern State University of Louisiana, Natchitoches, LA 71457., USA, E-mail: galminas@nsula.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Northwestern State University of Louisiana, Natchitoches, LA 71457., USA, E-mail:","institution_ids":["https://openalex.org/I157717896"]},{"raw_affiliation_string":"Department of Mathematics, Northwestern State University of Louisiana, Natchitoches, LA 71457., USA, E-mail: galminas@nsula.edu","institution_ids":["https://openalex.org/I157717896"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057131001","display_name":"John W. Rosenthal","orcid":null},"institutions":[{"id":"https://openalex.org/I87424562","display_name":"Ithaca College","ror":"https://ror.org/01kw1gj07","country_code":"US","type":"education","lineage":["https://openalex.org/I87424562"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John W. Rosenthal","raw_affiliation_strings":["Department of Mathematics, Ithaca College, Ithaca. NY 14850, USA, E-mail:","Department of Mathematics, Ithaca College, Ithaca. NY 14850, USA, E-mail: rosentha@ithaca.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Ithaca College, Ithaca. NY 14850, USA, E-mail:","institution_ids":["https://openalex.org/I87424562"]},{"raw_affiliation_string":"Department of Mathematics, Ithaca College, Ithaca. NY 14850, USA, E-mail: rosentha@ithaca.edu","institution_ids":["https://openalex.org/I87424562"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5089817196"],"corresponding_institution_ids":["https://openalex.org/I157717896"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.15778322,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"67","issue":"2","first_page":"859","last_page":"878"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9965999722480774,"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":0.9965999722480774,"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":0.9959999918937683,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9642999768257141,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/undecidable-problem","display_name":"Undecidable problem","score":0.7797756195068359},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7739781737327576},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.7283729910850525},{"id":"https://openalex.org/keywords/algebraically-closed-field","display_name":"Algebraically closed field","score":0.5745929479598999},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5630391836166382},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.484452486038208},{"id":"https://openalex.org/keywords/recursively-enumerable-language","display_name":"Recursively enumerable language","score":0.46840283274650574},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.41657713055610657},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37277519702911377},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.31464993953704834},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.2556781768798828}],"concepts":[{"id":"https://openalex.org/C192034797","wikidata":"https://www.wikidata.org/wiki/Q3502995","display_name":"Undecidable problem","level":3,"score":0.7797756195068359},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7739781737327576},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.7283729910850525},{"id":"https://openalex.org/C203701370","wikidata":"https://www.wikidata.org/wiki/Q1047547","display_name":"Algebraically closed field","level":2,"score":0.5745929479598999},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5630391836166382},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.484452486038208},{"id":"https://openalex.org/C203702658","wikidata":"https://www.wikidata.org/wiki/Q1073063","display_name":"Recursively enumerable language","level":2,"score":0.46840283274650574},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.41657713055610657},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37277519702911377},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.31464993953704834},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.2556781768798828},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2178/jsl/1190150113","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1190150113","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:digitalcommons.ithaca.edu:scopus_articles-3184","is_oa":false,"landing_page_url":"https://digitalcommons.ithaca.edu/scopus_articles/2185","pdf_url":null,"source":{"id":"https://openalex.org/S4377196817","display_name":"Digital Collections - Ithaca College Library (Ithaca College)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I87424562","host_organization_name":"Ithaca College","host_organization_lineage":["https://openalex.org/I87424562"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Articles Indexed in Scopus","raw_type":"text"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1190150113","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1190150113","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W190247079","https://openalex.org/W395120016","https://openalex.org/W1161597127","https://openalex.org/W1963706220","https://openalex.org/W1977629364","https://openalex.org/W2000803808","https://openalex.org/W2000947982","https://openalex.org/W2025407611","https://openalex.org/W2025575556","https://openalex.org/W2027845361","https://openalex.org/W2035335672","https://openalex.org/W2035900838","https://openalex.org/W2041183232","https://openalex.org/W2042840821","https://openalex.org/W2044827312","https://openalex.org/W2047280602","https://openalex.org/W2049650104","https://openalex.org/W2056414301","https://openalex.org/W2062135743","https://openalex.org/W2070000691","https://openalex.org/W2074264372","https://openalex.org/W2144412048","https://openalex.org/W2213334677","https://openalex.org/W2213947234","https://openalex.org/W2745993813","https://openalex.org/W3150920821","https://openalex.org/W4230395524","https://openalex.org/W4232277851","https://openalex.org/W4255288880","https://openalex.org/W4301746773","https://openalex.org/W6742645173"],"related_works":["https://openalex.org/W2901084331","https://openalex.org/W1526277826","https://openalex.org/W2109115134","https://openalex.org/W2004744288","https://openalex.org/W2140392112","https://openalex.org/W1978292968","https://openalex.org/W3099922764","https://openalex.org/W2066136688","https://openalex.org/W1510002872","https://openalex.org/W2060473848"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"show":[2,112],"that":[3,35,42,74,113,165],"the":[4,9,43,48,83,114,119,140],"first":[5,37,44,76,98,115,167],"order":[6,38,45,77,99,116,168],"theory":[7,40,46],"of":[8,16,21,36,47,54,59,75,85,89,93,118,125,128,142,147,156,166],"lattice":[10,49,84,120,141],"<":[11],"\u03c9":[12,95],"(":[13,50,121],"S":[14,29,51,68],")":[15,53,124],"finite":[17,86],"dimensional":[18,25,63,87],"closed":[19,57,145,152],"subsets":[20,58],"any":[22,60],"nontrivial":[23,61],"infinite":[24,62,158],"Steinitz":[26,65],"Exhange":[27],"System":[28,67],"has":[30,70],"logical":[31,71,163],"complexity":[32,72,164],"at":[33],"least":[34],"number":[39,78,169],"and":[41,101,139],"\u221e":[52,69,123,138,155],"computably":[55],"enumerable":[56],"computable":[64],"Exchange":[66],"exactly":[73],"theory.":[79,170],"Thus,":[80],"for":[81],"example,":[82],"subspaces":[88,127],"a":[90,129,148],"standard":[91],"copy":[92],"\u2295":[94],"Q":[96],"interprets":[97],"arithmetic":[100],"is":[102],"therefore":[103],"as":[104,106],"complicated":[105],"possible.":[107],"In":[108],"particular,":[109],"our":[110],"results":[111],"theories":[117],"V":[122,137],"c.e.":[126,143],"fully":[130,149],"effective":[131,150],"\u2135":[132],"0":[133],"-dimensional":[134],"vector":[135],"space":[136],"algebraically":[144,151],"subfields":[146],"field":[153],"F":[154],"countably":[157],"transcendence":[159],"degree":[160],"each":[161],"have":[162]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}