论文标题
矢量的无限块序列的参数化拉姆西理论
Parametrized Ramsey theory of infinite block sequences of vectors
论文作者
论文摘要
我们表明，Gowers的$ \ Mathrm {fin} _K $和$ \ Mathrm {fin} _ {\ pm k} $定理的无限维版本可以通过$ 2^ω$的完美子集的无限序列来参数。为此，我们使用Ultra-Ramsey理论获得了结果的精确和近似版本，该结果结合了Gowers定理和Hales-Jewett定理的元素。结果，我们获得了Gowers的$ C_0 $定理的参数化版本。
We show that the infinite-dimensional versions of Gowers' $\mathrm{FIN}_k$ and $\mathrm{FIN}_{\pm k}$ theorems can be parametrized by an infinite sequence of perfect subsets of $2^ω$. To do so, we use ultra-Ramsey theory to obtain exact and approximate versions of a result which combines elements from both Gowers' theorems and the Hales-Jewett theorem. As a consequence, we obtain a parametrized version of Gowers' $c_0$ theorem.
