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math.LO2025
Generalized Higman's Theorem and iterated ideals
Fedor Pakhomov, Giovanni Soldà
Generalized Higman's Theorem is the direct counterpart of Higman's Theorem that asserts the closure of the class of \emph{better} quasi-orders, instead of the class of \emph{well}…
math.LO2024
On Nash-Williams' Theorem regarding sequences with finite range
Fedor Pakhomov, Giovanni Soldà
The famous theorem of Higman states that for any well-quasi-order (wqo) the embeddability order on finite sequences over is also wqo. In his celebrated 1965 paper, Nash-Wil…
math.LO2024★ 1 cited
Sequential discontinuity and first-order problems
Arno Pauly, Giovanni Soldà
We explore the low levels of the structure of the continuous Weihrauch degrees of first-order problems. In particular, we show that there exists a minimal discontinuous first-order…