{"id":"https://openalex.org/W1978994835","doi":"https://doi.org/10.1002/malq.19970430105","title":"Strongly Amorphous Sets and Dual Dedekind Infinity","display_name":"Strongly Amorphous Sets and Dual Dedekind Infinity","publication_year":1997,"publication_date":"1997-01-01","ids":{"openalex":"https://openalex.org/W1978994835","doi":"https://doi.org/10.1002/malq.19970430105","mag":"1978994835"},"language":"en","primary_location":{"id":"doi:10.1002/malq.19970430105","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19970430105","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["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/A5067501710","display_name":"Martin Goldstern","orcid":"https://orcid.org/0000-0002-0438-633X"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Martin Goldstern","raw_affiliation_strings":["I am grateful to J. W. Degen for motivating me to write this paper, and to Norbert Brunner for carefully reading a draft version of this paper and suggesting many improvements","Institut fu\u0308r Algebra und Diskrete Mathematik, TU Wien, Wiedner Hauptstra\u00dfe 8-10/118.2, A-1040 Wien, Austria"],"affiliations":[{"raw_affiliation_string":"I am grateful to J. W. Degen for motivating me to write this paper, and to Norbert Brunner for carefully reading a draft version of this paper and suggesting many improvements","institution_ids":[]},{"raw_affiliation_string":"Institut fu\u0308r Algebra und Diskrete Mathematik, TU Wien, Wiedner Hauptstra\u00dfe 8-10/118.2, A-1040 Wien, Austria","institution_ids":["https://openalex.org/I145847075"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5067501710"],"corresponding_institution_ids":["https://openalex.org/I145847075"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.11235764,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"43","issue":"1","first_page":"39","last_page":"44"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9934999942779541,"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":0.9934999942779541,"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":0.9850999712944031,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9642999768257141,"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/mathematics","display_name":"Mathematics","score":0.8566015958786011},{"id":"https://openalex.org/keywords/dedekind-cut","display_name":"Dedekind cut","score":0.7982635498046875},{"id":"https://openalex.org/keywords/injective-function","display_name":"Injective function","score":0.7320740222930908},{"id":"https://openalex.org/keywords/power-set","display_name":"Power set","score":0.7238174080848694},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6084907054901123},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.49205702543258667},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.4801335036754608},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4741976857185364},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.4569123685359955},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4461379051208496},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.42889341711997986},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3748781085014343},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3315444588661194},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14407381415367126},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.08498305082321167},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05904674530029297},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.042034298181533813}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8566015958786011},{"id":"https://openalex.org/C76449584","wikidata":"https://www.wikidata.org/wiki/Q851333","display_name":"Dedekind cut","level":2,"score":0.7982635498046875},{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.7320740222930908},{"id":"https://openalex.org/C100643331","wikidata":"https://www.wikidata.org/wiki/Q205170","display_name":"Power set","level":3,"score":0.7238174080848694},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6084907054901123},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.49205702543258667},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.4801335036754608},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4741976857185364},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.4569123685359955},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4461379051208496},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.42889341711997986},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3748781085014343},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3315444588661194},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14407381415367126},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.08498305082321167},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05904674530029297},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.042034298181533813},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/malq.19970430105","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19970430105","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["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":7,"referenced_works":["https://openalex.org/W827220490","https://openalex.org/W1003365390","https://openalex.org/W1032030852","https://openalex.org/W1549237291","https://openalex.org/W1967842301","https://openalex.org/W2053778953","https://openalex.org/W2734670706"],"related_works":["https://openalex.org/W2080609356","https://openalex.org/W4233869232","https://openalex.org/W3101104522","https://openalex.org/W1454449932","https://openalex.org/W3023338730","https://openalex.org/W2235319579","https://openalex.org/W4289046789","https://openalex.org/W4313071721","https://openalex.org/W2510579135","https://openalex.org/W2771826017"],"abstract_inverted_index":{"Abstract":[0],"1.":[1],"If":[2],"A":[3,11],"is":[4,19,31,39],"strongly":[5],"amorphous":[6],"(i.e.,":[7],"all":[8],"relations":[9],"on":[10],"are":[12],"definable),":[13],"then":[14],"its":[15],"power":[16],"set":[17],"P(A)":[18,28,30],"dually":[20],"Dedekind":[21],"infinite,":[22],"i.":[23],"e.,":[24],"every":[25],"function":[26],"from":[27],"onto":[29],"injective.":[32],"2.":[33],"The":[34],"class":[35],"of":[36],"\u201cinexhaustible\u201d":[37],"sets":[38],"not":[40],"closed":[41],"under":[42],"supersets":[43],"unless":[44],"AC":[45],"holds.":[46]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}