On Erdos--Dushnik--Miller theorem without AC
Logic
2023-09-13 v4 Combinatorics
General Topology
Group Theory
Abstract
In set theory without the Axiom of Choice, we study the possible placement of Erdos-Dushnik-Miller theorem restricted to an uncountable set of vertices in the hierarchy of weak choice forms. We also answer a part of a question raised by Lajos Soukup.
Cite
@article{arxiv.2211.05665,
title = {On Erdos--Dushnik--Miller theorem without AC},
author = {Amitayu Banerjee and Alexa Gopaulsingh},
journal= {arXiv preprint arXiv:2211.05665},
year = {2023}
}
Comments
This version of the manuscript is accepted in a Journal (a few changes in claim 5.3 from arXiv version 3). arXiv admin note: text overlap with arXiv:2109.05914