数理逻辑
2008-5
世界图书出版公司
艾宾浩斯 (Ebbinghaus H.D.),J. Flum,W. Thomas
289
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What is a mathematical proof? How can proofs be justified? Are there limitations to provability? To what extent can machines carry out mathematical proofs? Only in this century has there been success in obtaining substantial and satisfactory answers. The present book contains a systematic discussion of these results. The investigations are centered around first-order logic. Our first goal is Godels completeness theorem， which shows that the consequence relation coincides with formal provability： By means of a calculus consisting of simple formal inference rules， one can obtain all consequences of a given axiom system (and in particular， imitate all mathematical proofs)
作者：(德国)艾宾浩斯(Ebbinghaus H.D.)
Preface PART A I Introduction 1.An Example from Group Theory 2.An Example from the Theory of Equivalence Relations 3.A Preliminary Analysis 4.Preview II Syntax of First-Order Languages 1.Alphabets 2.The Alphabet of a First-Order Language 3.Terms and Formulas in First-Order Languages 4.Induction in the Calculus of Terms and in the Calculus of Formulas 5.Free Variables and Sentences III Semantics of First-Order Languages 1.Structures and Interpretations 2.Standardization of Connectives 3.The Satisfaction Relation 4.The Consequence Relation 5.Two Lemmas on the Satisfaction Relation ……
《数理逻辑(第2版)》由世界图书出版公司出版。A short digression into model theory will help us to analyze the expressive power of the first-order language， and it will turn out that there are certain deficiencies. For example， the first-order language does not allow the formulation of an adequate axiom system for arithmetic or analysis. On the other hand， this di~~culty can be overcome——-even in the framework of first-order logic——by developing mathematics in set-theoretic terms. We explain the prerequisites from set theory necessary for this purpose and then treat the subtle relation between logic and set theory in a thorough manner.Godel‘s incompleteness theorems are presented in connection with several related results （such as Trahtenbrot’s theorem） which all exemplify the limitatious of machine-oriented proof methods. The notions of computability theory that are relevant to this discussion are given in detail.
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经典著作，偏数学的数理逻辑导论。
哥德尔完全性和不完全性的证明讲得非常透彻、细致，非常适合大学生阅读！！第二版加上了逻辑程序一章，使内容更加充实。
内容全面翔实，同样多的内容往常可能要用两三本数去凑——不是偏重语形就是偏重语义。
挺不错的，全英的啊。。。不过不是我看到，我男友看的，他说这本书很好！