论文标题
Ramsey理论分层半群
Ramsey theory for layered semigroups
论文作者
论文摘要
正如Farah，Hindman和McLeod所介绍的那样，我们进一步发展了分层的半群的理论，该理论提供了一个通用框架，以证明Ramsey关于这种Semigroup $ s $的陈述。根据非标准和拓扑论点，我们表明Ramsey在$ s $上的说法暗示了$ S $中的“连贯”序列。该框架使我们能够形式化并证明Ramsey理论的许多结果，包括Gowers的$ \ Mathrm {Fin} _K $ Theorem，Graham-Rothschild定理和Hindman的有限定理。其他亮点还包括：Graham-Rothschild定理的简单非标准证明强词；使用卡尔森，辛德曼和施特劳斯的结果，贝尔格森 - 布拉斯·辛德曼的分区定理的非标准证明；以及后一个结果和Gowers定理的共同概括，可以在我们的框架中证明。
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.
