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math.LO2025
Three forms of the ErdÅs-Dushnik-Miller Theorem
Paul Howard, Eleftherios Tachtsis
We continue the study of the ErdÅs-Dushnik-Miller theorem (A graph with an uncountable set of vertices has either an infinite independent set or an uncountable clique) in set theo…
math.LO2024
Maximal δ-separated sets in separable metric spaces and weak forms of choice
MichaŠDybowski, Przemyslaw Górka, Paul Howard
We show that the statement ``In every separable pseudometric space there is a maximal non-strictly δ-separated set.'' implies the axiom of choice for countable families of sets. T…