{"id":"https://openalex.org/W2061312397","doi":"https://doi.org/10.1007/s00153-004-0241-3","title":"Epsilon substitution for transfinite induction","display_name":"Epsilon substitution for transfinite induction","publication_year":2004,"publication_date":"2004-10-09","ids":{"openalex":"https://openalex.org/W2061312397","doi":"https://doi.org/10.1007/s00153-004-0241-3","mag":"2061312397"},"language":"en","primary_location":{"id":"doi:10.1007/s00153-004-0241-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00153-004-0241-3","pdf_url":null,"source":{"id":"https://openalex.org/S188076996","display_name":"Archive for Mathematical Logic","issn_l":"0933-5846","issn":["0933-5846","1432-0665"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Archive for Mathematical 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/A5047471753","display_name":"Henry Towsner","orcid":"https://orcid.org/0000-0001-7993-5148"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Henry Towsner","raw_affiliation_strings":["Carnegie Mellon, University","Carnegie Mellon"],"affiliations":[{"raw_affiliation_string":"Carnegie Mellon, University","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Carnegie Mellon","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5047471753"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.3454,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.62159978,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"44","issue":"4","first_page":"397","last_page":"412"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9703999757766724,"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":0.9703999757766724,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9685999751091003,"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/T11567","display_name":"semigroups and automata theory","score":0.9663000106811523,"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/substitution","display_name":"Substitution (logic)","score":0.8889836072921753},{"id":"https://openalex.org/keywords/transfinite-number","display_name":"Transfinite number","score":0.8097848892211914},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7268949747085571},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.47356975078582764},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.39221271872520447},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32723820209503174},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.24495801329612732},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16914144158363342},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.16806021332740784}],"concepts":[{"id":"https://openalex.org/C2778220771","wikidata":"https://www.wikidata.org/wiki/Q1522579","display_name":"Substitution (logic)","level":2,"score":0.8889836072921753},{"id":"https://openalex.org/C147358099","wikidata":"https://www.wikidata.org/wiki/Q1069891","display_name":"Transfinite number","level":2,"score":0.8097848892211914},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7268949747085571},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.47356975078582764},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.39221271872520447},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32723820209503174},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.24495801329612732},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16914144158363342},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.16806021332740784}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00153-004-0241-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00153-004-0241-3","pdf_url":null,"source":{"id":"https://openalex.org/S188076996","display_name":"Archive for Mathematical Logic","issn_l":"0933-5846","issn":["0933-5846","1432-0665"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Archive for Mathematical Logic","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.92.5701","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.92.5701","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.cmu.edu/users/hpt/pubs/esubTI.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W206702587","https://openalex.org/W1570072295","https://openalex.org/W1883089366","https://openalex.org/W1965834052","https://openalex.org/W1975810242","https://openalex.org/W2018493916","https://openalex.org/W2035851396","https://openalex.org/W2495407121","https://openalex.org/W4236235956"],"related_works":["https://openalex.org/W2089968568","https://openalex.org/W2048273249","https://openalex.org/W2950239705","https://openalex.org/W2261099788","https://openalex.org/W2498880115","https://openalex.org/W1663013072","https://openalex.org/W1864532727","https://openalex.org/W296787449","https://openalex.org/W3047919884","https://openalex.org/W2086359902"],"abstract_inverted_index":null,"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}