图书标签: 证明论 数理逻辑 数学 逻辑学 哲学 pl nemlophics Mathematics
发表于2024-11-07
Proof Theory pdf epub mobi txt 电子书 下载 2024
Focusing on Gentzen-type proof theory, this volume presents a detailed overview of creative works by author Gaisi Takeuti and other twentieth-century logicians. The text explores applications of proof theory to logic as well as other areas of mathematics. Suitable for advanced undergraduates and graduate students of mathematics, this long-out-of-print monograph forms a cornerstone for any library in mathematical logic and related topics.
The three-part treatment begins with an exploration of first order systems, including a treatment of predicate calculus involving Gentzen's cut-elimination theorem and the theory of natural numbers in terms of Gödel's incompleteness theorem and Gentzen's consistency proof. The second part, which considers second order and finite order systems, covers simple type theory and infinitary logic. The final chapters address consistency problems with an examination of consistency proofs and their applications.
叙述清晰凝练
评分书只看了不到三分之一,以后是不会再看了。书里有一些小错误。原来竹内外史是哥德尔的学生。跳着讲了切割消去证出一阶算术一致性,序数分析证了PA一致性,并且证明到epsilon0的超穷归纳是最经济的:前面的归纳都可以在PA中证明,但到epsilon0的标准ordering就无法在PA中证明了。
评分书只看了不到三分之一,以后是不会再看了。书里有一些小错误。原来竹内外史是哥德尔的学生。跳着讲了切割消去证出一阶算术一致性,序数分析证了PA一致性,并且证明到epsilon0的超穷归纳是最经济的:前面的归纳都可以在PA中证明,但到epsilon0的标准ordering就无法在PA中证明了。
评分书是好书,作者是好作者。但是尽管经过了多次修订,内容上依然还是有些旧。不过对于初学者来说已经足够了,也有一定的难度。对于高阶学者来说,基本上就是在复习proof theory一开始的abc,几乎完全没有涉及到80年代以后这个领域翻天覆地的变化。
评分书是好书,作者是好作者。但是尽管经过了多次修订,内容上依然还是有些旧。不过对于初学者来说已经足够了,也有一定的难度。对于高阶学者来说,基本上就是在复习proof theory一开始的abc,几乎完全没有涉及到80年代以后这个领域翻天覆地的变化。
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Proof Theory pdf epub mobi txt 电子书 下载 2024