论文标题
卡尔森 - 辛普森的引理和相反数学的应用
Carlson-Simpson's lemma and applications in reverse mathematics
论文作者
论文摘要
我们研究了由于卡尔森和辛普森而研究的Hales-Jewett定理的无限延伸的反向数学。这些定理在拉姆西理论中具有多个应用，例如无三角形图的有限大拉姆西数字或双重拉姆西定理。我们特别表明，开放的双ramsey定理在$ \ mathsf {aca}^{+} _ 0 $中包含。
We study the reverse mathematics of infinitary extensions of the Hales-Jewett theorem, due to Carlson and Simpson. These theorems have multiple applications in Ramsey's theory, such as the existence of finite big Ramsey numbers for the triangle-free graph, or the Dual Ramsey theorem. We show in particular that the Open Dual Ramsey theorem holds in $\mathsf{ACA}^{+}_0$.
