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Von Rimscha's Transitivity Conditions
Author(s) -
Howard Paul,
Rubin Jean E.,
Stanley Adrienne
Publication year - 2000
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/1521-3870(200010)46:4<549::aid-malq549>3.0.co;2-r
Subject(s) - mathematics , transitive relation , zermelo–fraenkel set theory , axiom of choice , urelement , set (abstract data type) , set theory , axiom , discrete mathematics , constructive set theory , combinatorics , mathematical economics , computer science , geometry , programming language
In Zermelo‐Fraenkel set theory with the axiom of choice every set has the same cardinal number as some ordinal. Von Rimscha has weakened this condition to “Every set has the same cardinal number as some transitive set”. In set theory without the axiom of choice, we study the deductive strength of this and similar statements introduced by von Rimscha.