Year: 2025
Type: article
Abstract: A set $A$ is dually Dedekind finite if every surjection from $A$ onto $A$ is injective; otherwise, $A$ is dually Dedekind infinite. It is proved consistent with $\mathsf{ZF}$ (i.e. the Zermelo–Fraenkel set theory without the axiom of choice) that there exists a family $\langle A_{n}\rangle _{n\in \omega }$ of sets such that, for all $n\in \omega $, $A_{n}^{n}$ is dually Dedekind finite whereas $A_{n}^{n+1}$ is dually Dedekind infinite. This resolves a question that was left open in (Classes of Dedekind finite cardinals. Fund. Math. 1974;84:187–208).
Source: Logic Journal of IGPL
Authors: Ruihuan Mao, Guozhen Shen
Institutions: Nankai University, Sun Yat-sen University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G4001432382
OpenAlex ID: W4414370495