2 problems

Let $K$ be an ultraproduct of the fields $\boldsymbol{Q}_{p_i}$ or $\boldsymbol{F}_{p_i}((t))$ over a non-principal ultrafilter, and let $\varphi(x,y)$ be a partitioned formula with…

Kalai–Meshulam's fractional Helly conjecture. There exists a function $\beta:(0,1)\to(0,1)$ such that, for every $\alpha>0$ and every sufficiently large set system $\mathcal{F}$ in…