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tourlakis g lectures logic set theory vol 1 mathematical logic 2003

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Textbook in PDF format 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

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Tourlakis G. Lectures in Logic and Set Theory. Vol 1. Mathematical Logic 2003.pdf 1.7 MB

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tourlakis g lectures logic set theory vol 1 mathematical logic 2003

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