分层半群的拉姆齐理论
Ramsey theory for layered semigroups
摘要：
我们进一步发展的理论分层半群，介绍了法拉，Hindman和McLeod，提供了一个通用的框架来证明拉姆齐声明这样的半群$S$。通过非标准和拓扑论证，证明了$S$上的Ramsey陈述是由$S$中“相干”序列的存在所隐含的.这个框架允许我们形式化和证明许多结果在拉姆齐理论，包括高尔斯的$\mathrm{FIN}_k$定理，格雷厄姆-罗斯柴尔德定理，和Hindman的有限和定理。其他亮点包括：一个简单的非标准证明的格雷厄姆-罗斯柴尔德定理强变量的话;一个非标准证明伯格森布拉斯-欣德曼的分区定理位于变量的话，使用的结果卡尔森，欣德曼和施特劳斯;和一个共同的概括后者的结果和高尔斯定理，这可以证明在我们的框架。
英文摘要：
We further develop the theory of layered semigroups, as introduced by Farah, Hindman and McLeod, providing a general framework to prove Ramsey statements about such a semigroup $S$. By nonstandard and topological arguments, we show Ramsey statements on $S$ are implied by the existence of "coherent" sequences in $S$. This framework allows us to formalise and prove many results in Ramsey theory, including Gowers' $\mathrm{FIN}_k$ theorem, the Graham-Rothschild theorem, and Hindman's finite sums theorem. Other highlights include: a simple nonstandard proof of the Graham-Rothschild theorem for strong variable words; a nonstandard proof of Bergelson-Blass-Hindman's partition theorem for located variable words, using a result of Carlson, Hindman and Strauss; and a common generalisation of the latter result and Gowers' theorem, which can be proven in our framework.
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