发表于2024-11-08
A Course in Mathematical Logic for Mathematicians 2024 pdf epub mobi 电子书
图书标签: 数理逻辑 数学 逻辑 Mathematical_Logic Logic 逻辑学 ebooks Mathematics
The book starts with an elementary introduction to formal languages appealing to the intuition of working mathematicians and unencumbered by philosophical or normative prejudices such as those of constructivism or intuitionism. It proceeds to the Proof Theory and presents several highlights of Mathematical Logic of 20th century: Gödel's and Tarski's Theorems, Cohen's Theorem on the independence of Continuum Hypothesis. Unusual for books on logic is a section dedicated to quantum logic. Then the exposition moves to the Computability Theory, based on the notion of recursive functions and stressing number{theoretic connections. A complete proof of Davis{Putnam{Robinson{Matiyasevich theorem is given, as well as a proof of Higman's theorem on recursive groups. Kolmogorov complexity is treated. The third Part of the book establishes essential equivalence of proof theory and computation theory and gives applications such as Gödel's theorem on the length of proofs. The new Chapter IX, written for the second edition, treats, among other things, categorical approach to the theory of computation, quantum computation, and P/NP problem. The new Chapter X, written for the second edition by Boris Zilber, contains basic results of Model Theory and its applications to mainstream mathematics. This theory found deep applications in algebraic and Diophantine geometry. Yuri Ivanovich Manin is Professor Emeritus at Max-Planck-Institute for Mathematics in Bonn, Germany, Board of Trustees Professor at the Northwestern University, Evanston, USA, and Principal Researcher at the Steklov Institute of Mathematics, Moscow, Russia. Boris Zilber, Professor of Mathematics at the University of Oxford, has been added to the second edition.
可作为课外读物,但不适合用作教科书。
评分可作为课外读物,但不适合用作教科书。
评分这是一本非同寻常的现代数理逻辑教科书。它起源于Manin自学逻辑的记录,从行文可看出作者的思维方式。作者指出了现代数理逻辑的三个生长点:模型论及其在代数、代数几何、算术几何、算子代数、动力系统中的运用;高阶范畴及其逻辑;理论计算机科学。本书最后一章强调了第一个方向(实际是Boris Zilber写的),而Manin-Marcolli最近几年文章则集中于后两个方向。
评分可作为课外读物,但不适合用作教科书。
评分可作为课外读物,但不适合用作教科书。
A Course in Mathematical Logic for Mathematicians 2024 pdf epub mobi 电子书