D'avid Uhrik

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math.LO2023

Complete Bipartite Partition Relations in Cohen Extensions

Dávid Uhrik

We investigate the effect of adding $ω_{2}$ Cohen reals on graphs on $ω_{2}$ , in particular we show that $ω_{2} \to (ω_{2}, ω : ω)^{2}$ holds after forcing with $Add (ω, ω_{2})$ in a mo…

math.LO2022

The Uncountable Hadwiger Conjecture and Characterizations of Trees Using Graphs

Dávid Uhrik

We prove that the existence of a non-special tree of size $λ$ is equivalent to the existence of an uncountably chromatic graph with no $K_{ω_{1}}$ minor of size $λ$ , establishing a c…