{"id":"https://openalex.org/W1987377250","doi":"https://doi.org/10.1002/malq.19950410111","title":"On \u03a3<sub>1</sub>\u2010definable Functions Provably Total in I \u220f","display_name":"On \u03a3<sub>1</sub>\u2010definable Functions Provably Total in I \u220f","publication_year":1995,"publication_date":"1995-01-01","ids":{"openalex":"https://openalex.org/W1987377250","doi":"https://doi.org/10.1002/malq.19950410111","mag":"1987377250"},"language":"en","primary_location":{"id":"doi:10.1002/malq.19950410111","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19950410111","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/A5091080470","display_name":"Teresa Bigorajska","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Teresa Bigorajska","raw_affiliation_strings":["Katedra Matematyki i Fizyki WSRP w Siedlcach, ul. Orlicz-Dreszera 19/21, 08\u2013110 Siedlce, Poland","Katedra Matematyki i Fizyki WSRP w Siedlcach, ul. Orlicz\u2010Dreszera 19/21, 08\u2013110 Siedlce, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Katedra Matematyki i Fizyki WSRP w Siedlcach, ul. Orlicz-Dreszera 19/21, 08\u2013110 Siedlce, Poland","institution_ids":[]},{"raw_affiliation_string":"Katedra Matematyki i Fizyki WSRP w Siedlcach, ul. Orlicz\u2010Dreszera 19/21, 08\u2013110 Siedlce, Poland","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5091080470"],"corresponding_institution_ids":[],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.5357,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.58443987,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"41","issue":"1","first_page":"135","last_page":"137"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9876000285148621,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9876000285148621,"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":0.9839000105857849,"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"}},{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9743000268936157,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/mathematics","display_name":"Mathematics","score":0.8504695892333984},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.63605135679245},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6171036958694458},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.5773452520370483},{"id":"https://openalex.org/keywords/unit","display_name":"Unit (ring theory)","score":0.5708596706390381},{"id":"https://openalex.org/keywords/commutative-ring","display_name":"Commutative ring","score":0.5124614834785461},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.4323442578315735},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4101662039756775},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10518914461135864}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8504695892333984},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.63605135679245},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6171036958694458},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.5773452520370483},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.5708596706390381},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.5124614834785461},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4323442578315735},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4101662039756775},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10518914461135864},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/malq.19950410111","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19950410111","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":1,"referenced_works":["https://openalex.org/W1594785505"],"related_works":["https://openalex.org/W4308298797","https://openalex.org/W4255963200","https://openalex.org/W2360590989","https://openalex.org/W4255391830","https://openalex.org/W2369074270","https://openalex.org/W2408222820","https://openalex.org/W2741158649","https://openalex.org/W2253391970","https://openalex.org/W2953844587","https://openalex.org/W1565509971"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"prove":[2],"the":[3,14,17,29,108,113,123],"following":[4],"theorem:":[5],"Let":[6],"\u03c6(":[7,119],"x":[8,53,74,91,96,99,120,128],")":[9,33,54,60,66,97,121,131],"be":[10],"a":[11,81],"formula":[12],"in":[13],"language":[15],"of":[16,21,28,115,122],"theory":[18,109],"PA":[19,110],"\u2212":[20,106,111],"discretely":[22],"ordered":[23],"commutative":[24],"rings":[25],"with":[26,34,134],"unit":[27],"form":[30,124],"\u2203y\u03c6\u2032(":[31],"x,y":[32,59],"\u03c6\u2032":[35,135],"and":[36,41],"let":[37,42],"\u2208":[38,136],"\u0394":[39,137],"0":[40,138],"f":[43,50],"\u03c6:":[44],"\u2115":[45,47],"\u2192":[46],"such":[48,85],"that":[49,86],"\u03c6":[51,77],"(":[52],"=":[55],"y":[56,65,93,126,130],"iff":[57],"\u03c6\u2032(":[58,67,127],"&amp;":[61],"(\u2200":[62],"z":[63],"&lt;":[64,98],"x,z":[68],").":[69,101],"If":[70],"I":[71,87,103],"\u220f":[72,88,104],"\u2208(\u2200":[73],"\u2265":[75],"0),":[76],"then":[78],"there":[79],"exists":[80],"natural":[82],"number":[83],"K":[84,100],"\u22a2":[89],"\u2203y\u2200x(":[90],"&gt;":[92],"\u27f9":[94],"\u0192\u03c6(":[95],"Here":[102],"1":[105],"denotes":[107],"plus":[112],"scheme":[114],"induction":[116],"for":[117],"formulas":[118],"\u2200":[125],",":[129],"(with":[132],"\u03c6\u2032)":[133],".":[139]},"counts_by_year":[{"year":2014,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}