{"id":"https://openalex.org/W1219408972","doi":"https://doi.org/10.3233/com-150036","title":"Some new results in monadic second-order arithmetic","display_name":"Some new results in monadic second-order arithmetic","publication_year":2015,"publication_date":"2015-07-01","ids":{"openalex":"https://openalex.org/W1219408972","doi":"https://doi.org/10.3233/com-150036","mag":"1219408972"},"language":"en","primary_location":{"id":"doi:10.3233/com-150036","is_oa":false,"landing_page_url":"https://doi.org/10.3233/com-150036","pdf_url":null,"source":{"id":"https://openalex.org/S4210231662","display_name":"Computability","issn_l":"2211-3568","issn":["2211-3568","2211-3576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computability","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/A5006401614","display_name":"Stanislav O. Speranski","orcid":"https://orcid.org/0000-0001-6386-5632"},"institutions":[{"id":"https://openalex.org/I4210096862","display_name":"Sobolev Institute of Mathematics","ror":"https://ror.org/00shc0s02","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I1313323035","https://openalex.org/I4210096862","https://openalex.org/I4210124601","https://openalex.org/I4210127387"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Stanislav O. Speranski","raw_affiliation_strings":["Sobolev Institute of Mathematics, Novosibirsk, Russia. ","Sobolev Institute of Mathematics, Novosibirsk, Russia. katze.tail@gmail.com"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sobolev Institute of Mathematics, Novosibirsk, Russia. ","institution_ids":["https://openalex.org/I4210096862"]},{"raw_affiliation_string":"Sobolev Institute of Mathematics, Novosibirsk, Russia. katze.tail@gmail.com","institution_ids":["https://openalex.org/I4210096862"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5006401614"],"corresponding_institution_ids":["https://openalex.org/I4210096862"],"apc_list":null,"apc_paid":null,"fwci":0.3634,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.62893398,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"4","issue":"2","first_page":"159","last_page":"174"},"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/T11567","display_name":"semigroups and automata theory","score":0.9993000030517578,"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":0.998199999332428,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.795211672782898},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5651808381080627},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4572950601577759},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4173756241798401},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.09468501806259155}],"concepts":[{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.795211672782898},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5651808381080627},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4572950601577759},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4173756241798401},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.09468501806259155},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/com-150036","is_oa":false,"landing_page_url":"https://doi.org/10.3233/com-150036","pdf_url":null,"source":{"id":"https://openalex.org/S4210231662","display_name":"Computability","issn_l":"2211-3568","issn":["2211-3568","2211-3576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computability","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":12,"referenced_works":["https://openalex.org/W239849515","https://openalex.org/W1965611063","https://openalex.org/W1970395543","https://openalex.org/W1980102547","https://openalex.org/W2014920673","https://openalex.org/W2015376829","https://openalex.org/W2031648800","https://openalex.org/W2033524652","https://openalex.org/W2034177508","https://openalex.org/W2099198433","https://openalex.org/W2138856440","https://openalex.org/W2162583406"],"related_works":["https://openalex.org/W2054384926","https://openalex.org/W2118359714","https://openalex.org/W2562957045","https://openalex.org/W2345600497","https://openalex.org/W241866648","https://openalex.org/W2142041376","https://openalex.org/W4247778000","https://openalex.org/W2626380860","https://openalex.org/W2047454787","https://openalex.org/W2058171746"],"abstract_inverted_index":{"Abstract":[0],"Let":[1],"\u03c3":[2],"be":[3,140],"a":[4,10,19,78,89,133],"signature":[5,207],"and":[6,41,99,120,127,165,175],"[Formula:":[7,14,24,32,36,59,65,69,84,90,104,110,114,137,147,154,162,167,172,176,182,186],"see":[8,15,25,33,37,60,66,70,85,91,105,111,115,138,148,155,163,168,173,177,183,187],"text]":[9,26,34,38,67,139,149,164,169,174,184],"\u03c3-structure":[11],"with":[12,35],"domain":[13],"text].":[16,116,156,188],"Say":[17],"that":[18,204],"monadic":[20],"second-order":[21],"\u03c3-formula":[22],"is":[23,68,83,109,208],"iff":[27],"it":[28,108],"has":[29,185],"the":[30,48,56,94,124,128,141,200,205],"form":[31],"set":[39,45,57,79],"variables":[40],"\u03c8":[42],"containing":[43],"no":[44],"quantifiers.":[46],"Consider":[47],"following":[49],"properties:":[50],"for":[51,72],"each":[52,73],"positive":[53,74],"integer":[54,75],"n,":[55,76],"of":[58,80,97,103,150,199],"text]-":[61],"\u03c3-sentences":[62],"true":[63],"in":[64,93,113,179],"text]-complete;":[71],"if":[77],"natural":[81,151],"numbers":[82,152],"text]-definable":[86,112],"(i.e.":[87],"by":[88],"text]-formula)":[92],"standard":[95],"model":[96],"arithmetic":[98],"closed":[100],"under":[101],"automorphisms":[102],"text],":[106],"then":[107],"We":[117],"use":[118],"\u2223":[119],"\u22a5":[121],"to":[122,195],"denote":[123],"divisibility":[125],"relation":[126,130],"coprimeness":[129],"respectively.":[131],"Given":[132],"prime":[134],"p,":[135],"let":[136],"function":[142],"which":[143],"maps":[144],"every":[145],"pair":[146],"into":[153],"In":[157],"this":[158],"article":[159],"we":[160],"prove:":[161],"all":[166],"have":[170],"both":[171],"text];":[178],"effect,":[180],"even":[181],"Notice":[189],"\u2013":[190],"these":[191],"results":[192],"readily":[193],"generalise":[194],"arbitrary":[196],"arithmetical":[197],"expansions":[198],"corresponding":[201],"structures,":[202],"provided":[203],"extended":[206],"finite.":[209]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2026-05-01T06:04:38.248271","created_date":"2025-10-10T00:00:00"}