Ya-Yi Fu

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math.LO2026

Enclosing a Compact Set in an O-minimal Expansion of $(R, +, \cdot, 0, 1 <)$

Yayi Fu

Fix an o-minimal expansion $R = (R, +, \cdot, 0, 1 <, ...)$ of the real ordered field. Given $C^{1}$ functions $f_{1}, ..., f_{k}$ , $g_{1}, ..., g_{k} : M \to R$ on a definable…

math.LO2026

Towards Trans-Exponential O-minimal Expansion of $(R, +, \cdot, 0, 1 <)$

Yayi Fu

We add an analytic trans-exponential function $φ$ to $R_{an, e x p}$ . We reduce the o-minimality of $R_{an, e x p, φ}$ to the existence of "many" regular values for so…

math.LO2023

A note on Erdős-Hajnal property for graphs with VC dimension $\leq 2$

Yayi Fu

Using techniques in \cite{chudnovsky2023erdHos} and substitution in \cite{alon2001ramsey}, we show that there is $ε > 0$ such that for any graph $G$ with VC-dimension $\leq 2$ , $G$ h…

math.LO2023

A model theoretic proof for o-minimal coherence theorem

Yayi Fu

Bakker, Brunebarbe, Tsimerman showed in \cite{bakker2022minimal} that the definable structure sheaf $O_{C^{n}}$ of $C^{n}$ is a coherent $\mathcal{O}_{\math…

math.LO2023

A note on strong Erdős-Hajnal for graphs with bounded VC-minimal complexity

Yayi Fu

Inspired by Adler's idea on VC minimal theories \cite{adler2008theories}, we introduce VC-minimal complexity. We show that for any $N \in N^{> 0}$ , there is $k_{N} > 0$ such that…

Enclosing a Compact Set in an O-minimal Expansion of (R,+,⋅,0,1<)

Towards Trans-Exponential O-minimal Expansion of (R,+,⋅,0,1<)

A note on Erdős-Hajnal property for graphs with VC dimension ≤2

A model theoretic proof for o-minimal coherence theorem

A note on strong Erdős-Hajnal for graphs with bounded VC-minimal complexity

Enclosing a Compact Set in an O-minimal Expansion of $(R, +, \cdot, 0, 1 <)$

Towards Trans-Exponential O-minimal Expansion of $(R, +, \cdot, 0, 1 <)$

A note on Erdős-Hajnal property for graphs with VC dimension $\leq 2$