Chieu-Minh Tran

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20242026

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5 papers · 1 filter

math.LO2026

Almost-linear Zarankiewicz bounds in $1$ -semi-equational theories

Hongyi Gou, Mostafa Mirabi, Mihir Mittal +2

We study multipartite hypergraphs definable in $1$ -semi\-equational theories and prove almost-linear Zarankiewicz bounds in every fixed arity $r \geq 2$ . More precisely, if $T$ is a…

math.LO2026

On Zarankiewicz's bounds for valued vector spaces

Hongyi Gou, Mihir Mittal, Chieu-Minh Tran +1

We establish absolute and relative almost-linear Zarankiewicz bounds for semilinear relations in valued vector spaces. For every fixed arity and description complexity, a $K_{t,\ld…

math.LO2026

Categoricity without Power

Jun Le Goh, Chieu-Minh Tran

We prove an analogue of Morley's categoricity theorem where cardinality is replaced by the recursion-theoretic notion of arithmetic degree. We say that a complete arithmetically de…

math.LO2026

Large implies henselian

Will Johnson, Chieu-Minh Tran, Erik Walsberg +1

Fix a field $K$ . We show that $K$ is large if and only if some elementary extension of $K$ is the fraction field of a henselian local domain which is not a field. The proof uses a…

math.LO2025

Of model completeness and algebraic groups

Daniel Max Hoffmann, Piotr Kowalski, Chieu-Minh Tran +1

We show that if G is a split semisimple algebraic group over a model complete field K, then the groups G(K) and G(K)' (the commutator group which is a ``Chevalley group'' as for ex…

Almost-linear Zarankiewicz bounds in 1-semi-equational theories

On Zarankiewicz's bounds for valued vector spaces

Categoricity without Power

Large implies henselian

Of model completeness and algebraic groups

Almost-linear Zarankiewicz bounds in $1$ -semi-equational theories