3 papers
math.LO2026
A choice-free proof of the Erdős--Dushnik--Miller theorem
Guozhen Shen
The Erdős--Dushnik--Miller theorem states that for every aleph , \[ κ\to(κ,ω); \] that is, every coloring has either a -homogeneous set of cardinality or a…
math.LO2025
Amorphous sets and dual Dedekind finiteness
Yifan Hu, Ruihuan Mao, Guozhen Shen
A set is dually Dedekind finite if every surjection from onto is injective; otherwise, is dually Dedekind infinite. An amorphous set is an infinite set that cannot…
math.LO2024
A note on dual Dedekind finiteness
Ruihuan Mao, Guozhen Shen
A set is dually Dedekind finite if every surjection from onto is injective; otherwise, is dually Dedekind infinite. It is proved consistent with (i.e.…