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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.
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
Defined Symbols
Computability and Uncomputability
Arithmetic, Definability, Undefinability and Incompletableness
Exercises
The Second Incompleteness Theorem
Peano Arithmetic
A Formal β-Function
Formal Primitive Recursion
The Boldface Arithmetization
Derivability Conditions Fixed Points
Exercises