AI 中文总结
研究利用非标准分析中的超自然数在算术拉姆齐理论中的应用，通过引入基本概念并举例，给出相关结果的非标准证明及新定理。
AI 中文摘要
非标准分析中的超自然数$\mathbb{N}$最近被证明是算术拉姆齐理论中的有效工具。引入基本的“非标准”概念后，给出几个例子说明该技术的实际应用。特别给出一些关于某些无限构型族的划分正则性的近期结果的简短非标准证明，还给出一个关于单色和与积的新定理。
英文摘要
The hypernatural numbers ${}^*\mathbb{N}$ of nonstandard analysis have recently proven to be an effective tool in arithmetic Ramsey theory. After introducing the fundamental ``nonstandard" notions, we present several examples to illustrate the use of this technique in practice. In particular, we provide brief nonstandard proofs of some recent results concerning the monochromaticity of certain families of finite and infinite configurations.
CommentsRewritten Section 7.1. To appear in the volume "Perspectives on Ergodic Theory and Its Interactions - In Honor of Vitaly Bergelson."
