Lectures in Logic and Set Theory : Mathematical Logic (Cambridge Studies in Advanced Mathematics) 〈1〉

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Lectures in Logic and Set Theory : Mathematical Logic (Cambridge Studies in Advanced Mathematics) 〈1〉

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  • 製本 Hardcover:ハードカバー版/ページ数 300 p.
  • 言語 ENG,ENG
  • 商品コード 9780521753739
  • DDC分類 511.3

基本説明

New in paperback. Hardcover was published in 2003.

Full Description


This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a user-friendly conversational lecture style that makes them equally effective for self-study or class use. Volume 1 includes formal proof techniques, a section on applications of compactness (including nonstandard analysis), a generous dose of computability and its relation to the incompleteness phenomenon, and the first presentation of a complete proof of Godel's 2nd incompleteness since Hilbert and Bernay's Grundlagen theorem.

Table of Contents

Preface                                            ix
Basic Logic 1 (204)
First Order Languages 5 (14)
A Digression into the Metatheory: 19 (9)
Informal Induction and Recursion
Axioms and Rules of Inference 28 (14)
Basic Metatheorems 42 (10)
Semantics; Soundness, Completeness, 52 (23)
Compactness
Substructures, Diagrams, and Applications 75 (37)
Defined Symbols 112(11)
Computability and Uncomputability 123(32)
Arithmetic, Definability, Undefinability, 155(36)
and Incompletableness
Exercises 191(14)
The Second Incompleteness Theorem 205(114)
Peano Arithmetic 206(26)
A Formal β-Function 232(16)
Formal Primitive Recursion 248(8)
The Boldface Δ and Σ 256(9)
Arithmetization 265(7)
Derivability Conditions; Fixed Points 272(44)
Exercises 316(3)
Bibliography 319(2)
List of Symbols 321(2)
Index 323