Subsystems of Second Order Arithmetic 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024

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Simpson, Stephen G. 作者

译者

2009-5 出版日期

464 页数

$ 114.13 价格

丛书系列

9780521884396 图书编码

Subsystems of Second Order Arithmetic 在线电子书图书标签: 递归论反推数学综述数理逻辑数学可计算性 nemlophics ReverseMath

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Subsystems of Second Order Arithmetic 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

Subsystems of Second Order Arithmetic 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024

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Almost all of the problems studied in this book are motivated by an overriding foundational question: What are the appropriate axioms for mathematics? Through a series of case studies, these axioms are examined to prove particular theorems in core mathematical areas such as algebra, analysis, and topology, focusing on the language of second-order arithmetic, the weakest language rich enough to express and develop the bulk of mathematics. In many cases, if a mathematical theorem is proved from appropriately weak set existence axioms, then the axioms will be logically equivalent to the theorem. Furthermore, only a few specific set existence axioms arise repeatedly in this context, which in turn correspond to classical foundational programs. This is the theme of reverse mathematics, which dominates the first half of the book. The second part focuses on models of these and other subsystems of second-order arithmetic.

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