Gabriel Fernandes

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math.LO2026

Amenable C-sequences and ineffability in L

Gabriel Fernandes

We give a relative consistency counterexample to the conjecture of Inamdar and Rinot that every regular uncountable cardinal carrying no amenable C-sequence is ineffable in the con…

math.LO2024

Remarks on Halin's end-degree Conjecture

Gabriel Fernandes

We prove new instances of Halin's end degree conjecture (HC) in ZFC. In particular, we show that there is a proper class of cardinals kappa for which Halin's conjecture holds, answ…

math.LO2024

Ray inflations of $ω_{1}$ -trees and ends of degree $ℵ_{1}$

Leandro Aurichi, Gabriel Fernandes, Paulo Magalhães Júnior

We prove the followings result for ray inflations of sparse graphs on $ω_{1}$ -trees. First, let $T$ and $S$ be pruned $ω_{1}$ -trees, let $G_{T}$ be a sparse $T$ -graph, and let $G_{S}$ be a…

Amenable C-sequences and ineffability in L

Remarks on Halin's end-degree Conjecture

Ray inflations of ω1​-trees and ends of degree ℵ1​

Ray inflations of $ω_{1}$ -trees and ends of degree $ℵ_{1}$