Subsystems of Second Order Arithmetic 2024 pdf epub mobi 电子书

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发表于2024-11-22

Subsystems of Second Order Arithmetic 2024 pdf epub mobi 电子书

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出版者:

作者:Simpson, Stephen G.

出品人:

页数:464

译者:

出版时间:2009-5

价格:$ 114.13

装帧:

isbn号码:9780521884396

丛书系列:

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

Subsystems of Second Order Arithmetic 2024 pdf epub mobi 电子书图书描述

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 2024 pdf epub mobi 电子书

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