Abstract
In ZFC set theory (i.e., Zermelo-Fraenkel set theory with the Axiom of Choice (AC)) any two cardinal numbers are comparable. However, this may not be valid in ZF (i.e., Zermelo-Fraenkel set theory modulo AC). In this paper, we study the strength of the inequality α2 < 2α (in ZF, for every infinite cardinal number α, 2α ≰ α2; see [13]), where α is either the cardinality of special sets (see Definition 1 below) which are expressed as disjoint unions of finite, pairwise equipotent, sets lacking choice functions, or the cardinality of sets in specific permutation models of ZF0 set theory (i.e., ZF without the Axiom of Regularity).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
