An Introduction to Metalogic

Aladdin M. Yaqub (Autor)

Buch | Softcover

310 Seiten

2014
Broadview Press Ltd (Verlag)
978-1-55481-171-7 (ISBN)

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Offers an accessible introduction to the metatheory of first-order predicate logic. No background knowledge of logic is presupposed, as the book is entirely self-contained and clearly defines all of the technical terms it employs. Yaqub begins with an introduction to predicate logic, and ends with detailed outlines of the proofs of the incompleteness, undecidability and indefinability theorems.

An Introduction to Metalogic is a uniquely accessible introduction to the metatheory of first-order predicate logic. No background knowledge of logic is presupposed, as the book is entirely self-contained and clearly defines all of the technical terms it employs. Yaqub begins with an introduction to predicate logic and ends with detailed outlines of the proofs of the incompleteness, undecidability, and indefinability theorems, covering many related topics in between.

Aladdin M. Yaqub is Professor of Philosophy at Lehigh University and the author of An Introduction to Logical Theory, The Liar Speaks the Truth, and a new translation of Al-Ghazali’s Moderation in Belief.

Introduction
Chapter One: First-Order Predicate Logic
1. The Syntax of PL
2. The Semantics of PL
3. Logical Concepts in PL
4. PL Proof Theory
5. Exercises
Chapter Two: Resources of the Metatheory
1. Linguistic and Logical Resources
2. Arithmetical Resources
3. Set-Theoretic Resources
4. An Economical Version of PL
5. Exercises
Chapter Three: The Soundness and Completeness Theorems
1. The Soundness Theorem
2. The Completeness Theorem
3. The Compactness Theorem
4. PL Interpretations and PL Sets
5. The Löwenheim-Skolem Theorem
6. Exercises
Chapter Four: Computability
1. Effective Procedures and Computable Functions
2. Turing Computability
3. The Halting Problem
4. Partial Recursive Functions
5. Exercises
Chapter Five: The Incompleteness Theorems
1. Peano Arithmetic
2. Representability in Peano Arithmetic
3. The Arithmetization of the Metatheory
4. Diagonalization and the First Incompleteness Theorem
5. Consequences of Diagonalization and Incompleteness
6. The Incompleteness of Second-Order Predicate Logic
7. Gödel's Second Incompleteness Theorem
8. Exercises

Sprache	englisch
Maße	178 x 229 mm
Themenwelt	Geisteswissenschaften ► Philosophie ► Logik
Themenwelt	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
ISBN-10	1-55481-171-6 / 1554811716
ISBN-13	978-1-55481-171-7 / 9781554811717
Zustand	Neuware