2024/12/10 by Ruihuan Mao, Mao, Ruihuan, Guozhen Shen +1 · 1 citation
Mathematics · #03E25 #Advanced Topology and Set Theory #FOS: Mathematics #Limits and Structures in Graph Theory #Logic (math.LO) #Primary 03E35 #Secondary 03E10
paper · pdf · doi:10.48550/arxiv.2412.07142
openalex publication_date 2024/12/10 · openalex created_date 2024/12/12 · openalex updated_date 2026/07/28
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 ZF (i.e., the Zermelo--Fraenkel set theory without the axiom of choice) that there exists a family ⟨ An⟩n∈ω of sets such that, for all n∈ω, Ann is dually Dedekind finite whereas Ann+1 is dually Dedekind infinite. This resolves a question that was left open in [J. Truss, Fund. Math. 84, 187--208 (1974)].