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El. knyga: Lectures in Logic and Set Theory: Volume 1, Mathematical Logic

(York University, Toronto)

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This two-volume set bridges the gap between introductory texts and the research literature.

This two-volume work bridges the gap between introductory expositions of logic (or set theory) and the research literature. 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 lecture style that makes them equally effective for self-study or class use. Volume I includes formal proof techniques, applications of compactness (including nonstandard analysis), computability and its relation to the completeness phenonmenon, and the first presentation of a complete proof of Godel's 2nd incompleteness since Hilbert and Bernay's Grundlagen.

Recenzijos

Review of the hardback: ' stands among the dozen or so books that will remain within easy reach from my desk a highly worthwhile addition to the literature.' The Review of Modern Logic

Daugiau informacijos

This two-volume set bridges the gap between introductory texts and the research literature.
Preface ix
Basic Logic
1(204)
First Order Languages
5(14)
A Digression into the Metatheory: Informal Induction and Recursion
19(9)
Axioms and Rules of Inference
28(14)
Basic Metatheorems
42(10)
Semantics; Soundness, Completeness, Compactness
52(23)
Substructures, Diagrams, and Applications
75(37)
Defined Symbols
112(11)
Computability and Uncomputability
123(32)
Arithmetic, Definability, Undefinability, and Incompletableness
155(36)
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