{"id":"https://openalex.org/W3081331081","doi":"https://doi.org/10.1017/s1755020320000301","title":"A NOTE ON CHOICE PRINCIPLES IN SECOND-ORDER LOGIC","display_name":"A NOTE ON CHOICE PRINCIPLES IN SECOND-ORDER LOGIC","publication_year":2020,"publication_date":"2020-08-25","ids":{"openalex":"https://openalex.org/W3081331081","doi":"https://doi.org/10.1017/s1755020320000301","mag":"3081331081"},"language":"en","primary_location":{"id":"doi:10.1017/s1755020320000301","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s1755020320000301","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/A5060082661","display_name":"Benjamin Siskind","orcid":"https://orcid.org/0000-0002-9256-6401"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"BENJAMIN SISKIND","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048685622","display_name":"Pietro Mancosu","orcid":"https://orcid.org/0000-0002-0165-7931"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"PAOLO MANCOSU","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5003405620","display_name":"Stewart Shapiro","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"STEWART SHAPIRO","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5060082661"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1444,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.53771127,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"16","issue":"2","first_page":"339","last_page":"350"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9951000213623047,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9951000213623047,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9933000206947327,"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/T10258","display_name":"Philosophy and Theoretical Science","score":0.989799976348877,"subfield":{"id":"https://openalex.org/subfields/3205","display_name":"Experimental and Cognitive Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6073591113090515},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.5973876714706421},{"id":"https://openalex.org/keywords/ackermann-function","display_name":"Ackermann function","score":0.5681544542312622},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.5460571646690369},{"id":"https://openalex.org/keywords/dynamic-logic","display_name":"Dynamic logic (digital electronics)","score":0.5196065306663513},{"id":"https://openalex.org/keywords/conservative-extension","display_name":"Conservative extension","score":0.5180807113647461},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5055594444274902},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.48578622937202454},{"id":"https://openalex.org/keywords/second-order-logic","display_name":"Second-order logic","score":0.4695870280265808},{"id":"https://openalex.org/keywords/higher-order-logic","display_name":"Higher-order logic","score":0.3790838420391083},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.3748219907283783},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.29204249382019043},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2656554877758026},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.23274105787277222},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.15154969692230225},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12301865220069885}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6073591113090515},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.5973876714706421},{"id":"https://openalex.org/C33436860","wikidata":"https://www.wikidata.org/wiki/Q341835","display_name":"Ackermann function","level":3,"score":0.5681544542312622},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5460571646690369},{"id":"https://openalex.org/C2777796570","wikidata":"https://www.wikidata.org/wiki/Q2351326","display_name":"Dynamic logic (digital electronics)","level":4,"score":0.5196065306663513},{"id":"https://openalex.org/C2780432614","wikidata":"https://www.wikidata.org/wiki/Q864213","display_name":"Conservative extension","level":2,"score":0.5180807113647461},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5055594444274902},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.48578622937202454},{"id":"https://openalex.org/C144791301","wikidata":"https://www.wikidata.org/wiki/Q1548746","display_name":"Second-order logic","level":4,"score":0.4695870280265808},{"id":"https://openalex.org/C169896238","wikidata":"https://www.wikidata.org/wiki/Q1644136","display_name":"Higher-order logic","level":3,"score":0.3790838420391083},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3748219907283783},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29204249382019043},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2656554877758026},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.23274105787277222},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.15154969692230225},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12301865220069885},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C172385210","wikidata":"https://www.wikidata.org/wiki/Q5339","display_name":"Transistor","level":3,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s1755020320000301","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s1755020320000301","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W4594304","https://openalex.org/W1960494084","https://openalex.org/W1984427300","https://openalex.org/W1997404494","https://openalex.org/W2026216944","https://openalex.org/W2039139196","https://openalex.org/W2051878948","https://openalex.org/W2058378008","https://openalex.org/W2122650439","https://openalex.org/W2328141028","https://openalex.org/W2502162402","https://openalex.org/W2989931657","https://openalex.org/W4210857673","https://openalex.org/W6660238100","https://openalex.org/W7046948909"],"related_works":["https://openalex.org/W2006286500","https://openalex.org/W2142816242","https://openalex.org/W1518114393","https://openalex.org/W1981373951","https://openalex.org/W1580672106","https://openalex.org/W4381707876","https://openalex.org/W4387318785","https://openalex.org/W2585206901","https://openalex.org/W1482260388","https://openalex.org/W2524454306"],"abstract_inverted_index":{"Abstract":[0],"Zermelo\u2019s":[1],"Theorem":[2],"that":[3,13,38],"the":[4,11,53,70,92],"axiom":[5],"of":[6,43],"choice":[7,50,62,78],"is":[8,63,89],"equivalent":[9],"to":[10,81],"principle":[12],"every":[14],"set":[15],"can":[16],"be":[17],"well-ordered":[18],"goes":[19],"through":[20],"in":[21,25,39],"third-order":[22,48],"logic,":[23,49],"but":[24],"second-order":[26,44,59,67],"logic":[27,45,60,68],"we":[28,36],"run":[29],"into":[30],"expressivity":[31],"issues.":[32],"In":[33],"this":[34,57],"note,":[35],"show":[37],"a":[40,76],"natural":[41],"extension":[42],"weaker":[46],"than":[47],"still":[51],"implies":[52,87],"well-ordering":[54,71,93],"principle.":[55,72,94],"Moreover,":[56],"extended":[58],"with":[61,69],"conservative":[64],"over":[65],"ordinary":[66],"We":[73],"also":[74],"discuss":[75],"variant":[77],"principle,":[79],"due":[80],"Hilbert":[82],"and":[83],"Ackermann,":[84],"which":[85],"neither":[86],"nor":[88],"implied":[90],"by":[91]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-03-14T08:43:22.919905","created_date":"2025-10-10T00:00:00"}
