{"title":"Review of An Introduction to Ramsey Theory: Fast Functions, Infinity, and Metamathematics by Matthew Katz and Jan Reimann","authors":"W. Gasarch","doi":"10.1145/3351452.3351456","DOIUrl":null,"url":null,"abstract":"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!","PeriodicalId":22106,"journal":{"name":"SIGACT News","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2019-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIGACT News","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3351452.3351456","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
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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