{"id":"https://openalex.org/W4383722132","doi":"https://doi.org/10.1017/s1755020323000217","title":"A SIMPLIFIED PROOF OF THE EPSILON THEOREMS","display_name":"A SIMPLIFIED PROOF OF THE EPSILON THEOREMS","publication_year":2023,"publication_date":"2023-07-10","ids":{"openalex":"https://openalex.org/W4383722132","doi":"https://doi.org/10.1017/s1755020323000217"},"language":"en","primary_location":{"id":"doi:10.1017/s1755020323000217","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s1755020323000217","pdf_url":null,"source":{"id":"https://openalex.org/S24077076","display_name":"The Review of Symbolic Logic","issn_l":"1755-0203","issn":["1755-0203","1755-0211"],"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":"The Review 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/A5058192101","display_name":"Stefan Hetzl","orcid":"https://orcid.org/0000-0002-6461-5982"},"institutions":[{"id":"https://openalex.org/I2799411422","display_name":"Center for Discrete Mathematics and Theoretical Computer Science","ror":"https://ror.org/00k551w06","country_code":"US","type":"facility","lineage":["https://openalex.org/I102322142","https://openalex.org/I118347220","https://openalex.org/I1283103587","https://openalex.org/I1311060795","https://openalex.org/I20089843","https://openalex.org/I2799411422","https://openalex.org/I4210107353"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"STEFAN HETZL","raw_affiliation_strings":["INSTITUTE OF DISCRETE MATHEMATICS AND GEOMETRY TU WIEN, WIEDNER HAUPTSTRASSE 8-10 1040 VIENNA, AUSTRIA URL: https://www.dmg.tuwien.ac.at/hetzl/"],"raw_orcid":"https://orcid.org/0000-0002-6461-5982","affiliations":[{"raw_affiliation_string":"INSTITUTE OF DISCRETE MATHEMATICS AND GEOMETRY TU WIEN, WIEDNER HAUPTSTRASSE 8-10 1040 VIENNA, AUSTRIA URL: https://www.dmg.tuwien.ac.at/hetzl/","institution_ids":["https://openalex.org/I2799411422"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5058192101"],"corresponding_institution_ids":["https://openalex.org/I2799411422"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07186562,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"4","first_page":"1248","last_page":"1263"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9990000128746033,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9990000128746033,"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/T12170","display_name":"History and Theory of Mathematics","score":0.9883999824523926,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/T12504","display_name":"Mathematics and Applications","score":0.9869999885559082,"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/mathematical-proof","display_name":"Mathematical proof","score":0.8372761011123657},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.6246558427810669},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6208360195159912},{"id":"https://openalex.org/keywords/associative-property","display_name":"Associative property","score":0.6083590984344482},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5319571495056152},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5072469115257263},{"id":"https://openalex.org/keywords/natural-deduction","display_name":"Natural deduction","score":0.4229912757873535},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.40469032526016235},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.365561306476593},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3145456910133362},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.04687979817390442}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.8372761011123657},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.6246558427810669},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6208360195159912},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.6083590984344482},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5319571495056152},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5072469115257263},{"id":"https://openalex.org/C62073222","wikidata":"https://www.wikidata.org/wiki/Q1572108","display_name":"Natural deduction","level":2,"score":0.4229912757873535},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.40469032526016235},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.365561306476593},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3145456910133362},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.04687979817390442},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s1755020323000217","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s1755020323000217","pdf_url":null,"source":{"id":"https://openalex.org/S24077076","display_name":"The Review of Symbolic Logic","issn_l":"1755-0203","issn":["1755-0203","1755-0211"],"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":"The Review of Symbolic Logic","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4399999976158142,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W104201083","https://openalex.org/W560364776","https://openalex.org/W1968350036","https://openalex.org/W1996404651","https://openalex.org/W2031927644","https://openalex.org/W2032033497","https://openalex.org/W2034155940","https://openalex.org/W2035851396","https://openalex.org/W2053289767","https://openalex.org/W2078109816","https://openalex.org/W2081602857","https://openalex.org/W2084443499","https://openalex.org/W2129156376","https://openalex.org/W2143374829","https://openalex.org/W2152535604","https://openalex.org/W2264007577","https://openalex.org/W2513373210","https://openalex.org/W2768246366","https://openalex.org/W2794392750","https://openalex.org/W3088532808","https://openalex.org/W3101828175","https://openalex.org/W4234048930","https://openalex.org/W4255132490","https://openalex.org/W4300885336"],"related_works":["https://openalex.org/W613892192","https://openalex.org/W1603543958","https://openalex.org/W179453746","https://openalex.org/W4390542336","https://openalex.org/W4232650499","https://openalex.org/W2155990634","https://openalex.org/W4232291640","https://openalex.org/W2162672092","https://openalex.org/W648111378","https://openalex.org/W1574493518"],"abstract_inverted_index":{"Abstract":[0],"We":[1,35],"formulate":[2],"Hilbert\u2019s":[3],"epsilon":[4,20,45],"calculus":[5,46],"in":[6,43],"the":[7,19,25,38,44],"context":[8],"of":[9,18,24,41],"expansion":[10],"proofs.":[11],"This":[12],"leads":[13],"to":[14],"a":[15],"simplified":[16],"proof":[17],"theorems":[21],"by":[22],"disposing":[23],"need":[26],"for":[27],"prenexification,":[28],"Skolemisation,":[29],"and":[30],"their":[31],"respective":[32],"inverse":[33],"transformations.":[34],"observe":[36],"that":[37],"natural":[39],"notion":[40],"cut":[42],"is":[47],"associative.":[48]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}