Jinhe Ye

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math.LO2025

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

When is $A + x A = R$

Jinhe Ye, Liang Yu, Xuanheng zhao

We show that there is an additive $F_{σ}$ subgroup $A$ of $R$ and $x \in R$ such that $di m_{H} (A) = \frac{1}{2}$ and $A + x A = R$ . However, if $A \…

math.LO2024

Zilber's Trichotomy in Hausdorff Geometric Structures

Benjamin Castle, Assaf Hasson, Jinhe Ye

We give a new axiomatic treatment of the Zilber trichotomy, and use it to complete the proof of the trichotomy for relics of algebraically closed fields, i.e., reducts of the ACF-i…

math.LO2024

Hyperbolicity and model-complete fields

Michał Szachniewicz, Jinhe Ye

We study model-complete fields that avoid a given quasi-project variety $V$ . There is a close connection between hyperbolicity of $V$ and the existence of the model companion for t…

math.LO2023

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…