Lectures in Logic and Set Theory

Volume 1 - Mathematical Logic

George Tourlakis

328 pages, parution le 17/03/2003

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Résumé

Lectures in Logic and Set Theory- Volume I

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 I 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.

Contents

I - Basic Logic
First Order Languages
A Digression into the Metatheory: Informal Induction and Recursion
Axioms and Rules of Inference
Basic Metatheorems
Semantics; Soundness, Completeness, Compactness
Substructures, Diagrams, and Applications
Denned Symbols
Computability and Uncomputability
Arithmetic, Definability, Undefinability, and Incompletableness
Exercises
II - The Second Incompleteness Theorem
Peano Arithmetic
A Formal ß-Function
Formal Primitive Recursion
The Boldface &delta and &epsilon
Arithmetization
Derivability Conditions; Fixed Points
Exercises
Bibliography
List of Symbols
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	George Tourlakis
Parution	17/03/2003
Nb. de pages	328
Format	15,5 x 23,5
Couverture	Relié
Poids	575g
Intérieur	Noir et Blanc
EAN13	9780521753739
ISBN13	978-0-521-75373-9