拉姆齐理论

Set Theory and Foundations of Mathematics: An Introduction to Mathematical Logic Pub Date : 2020-04-01 DOI:10.1142/9789811201936_0009

Justen Holl, Elizabeth Tso, Julia Balla, Fall

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摘要

拉姆齐理论研究的是特定模式如何在足够大的系统中不可避免地出现。本文概述了拉姆齐理论中的三个关键定理:拉姆齐定理、范德华登定理和拉多定理，它们分别处理在图形、数轴和线性方程组等数学对象中寻找模式的问题。虽然每个定理都截然不同，但它们都有一个共同的目标，即在混乱中辨别秩序。

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Ramsey Theory

Ramsey Theory is the study of how specific patterns inevitably emerge in sufficiently large systems. This paper provides an overview of three key theorems in Ramsey Theory: Ramsey’s Theorem, Van der Waerden’s Theorem, and Rado’s Theorem, which deal with finding patterns in mathematical objects such as graphs, the number line, and systems of linear equations respectively. While each theorem is distinctly different, they share a common objective of discerning order in chaos.

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Set Theory and Foundations of Mathematics: An Introduction to Mathematical Logic

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