《拉姆齐理论导论:快速函数、无穷和元数学》，作者:Matthew Katz和Jan Reimann

SIGACT News Pub Date : 2019-07-24 DOI:10.1145/3351452.3351456

W. Gasarch

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摘要

这是一个非常重要的定理，因为它表明皮亚诺算术不能做数论中的所有事情。然而，表述S是不自然的。帕里斯和哈林顿在拉姆齐理论中提出了一个在皮亚诺算术中无法证明的自然命题。我一直希望对Paris-Harrington结果有一个完整的解释，以及为什么它不能在皮亚诺算法中被证明。这本书是那种治疗方法吗?是的!

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Review of An Introduction to Ramsey Theory: Fast Functions, Infinity, and Metamathematics by Matthew Katz and Jan Reimann

This is a very important theorem since it shows that Peano Arithmetic cannot do everything in Number Theory. However, the statement S is not natural. Paris and Harrington came up with a natural statement in Ramsey Theory that is not provable in Peano Arithmetic. I have always wanted a clean self-contained treatment of the Paris-Harrington result and why it is not provable in Peano Arithmetic. Is this book that treatment? Yes!

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