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

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Simpson, Stephen G.

2009-5

464

$ 114.13

9780521884396

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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发表于2024-12-24

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

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

图书描述

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.

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