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Tourlakis, George
Mathematical Logic

1. Auflage September 2008
97,90 Euro
2008. 320 Seiten, Hardcover
ISBN 978-0-470-28074-4 - John Wiley & Sons

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Kurzbeschreibung
Mathematical logic is the art and science of mathematical reasoning. The only book written for the undergraduate logic user that is rigorous, correct, and user-friendly, Mathematical Logic presents mathematical or "symbolic" logic as a reliable tool for deductive reasoning in computer science, mathematics, philosophy, and other related disciplines. The book trains the reader in both the established "Hilbert" style as well as in the emerging "equational" style, enabling students in computer science and mathematics to become proficient users of logic.

Aus dem Inhalt
Preface.

Acknowledgments.

PART I: BOOLEAN LOGIC.

1. The Beginning.

1.1 Boolean Formulae.

1.2 Induction on the Complexity of WFF Some Easy Properties of WFF.

1.3 Inductive definitions on formulae.

1.4 Proofs and Theorems.

2. Theorems and Metatheorems.

2.1 More Hilbertstyle Proofs.

2.2 Equationalstyle Proofs.

2.3 Equational Proof Layout.

2.4 More Proofs; Enriching our Toolbox.

2.5 Using Special Axioms in Equational Proofs.

2.6 The Deduction Theorem.

3. The Interplay between Syntax and Semantics.

3.1 Soundness.

3.2 Post's Theorem.

3.3 Full Circle.

3.4 SingleFormula Leibniz.

3.5 Appendix: Resolution in Boolean Logic.

PART II: PREDICATE LOGIC.

4. Extending Boolean Logic.

4.1 The First Order Language of Predicate Logic.

4.2 Axioms and Rules of First Order Logic.

5 Two Equivalent Logics.

6. Generalisation and Additional Leibniz Rules.

6.1 Inserting and Removing "(8x)".

6.2 Leibniz Rules that Affect Quantifier Scopes.

6.3 The Leibniz Rules "8.12".

6.4 More Useful Tools.

6.5 Inserting and Removing "(9x)".

7. Properties of Equality.

8. First Order Semantics -- Very Naïvely.

8.1 Interpretations.

8.2 Soundness in Predicate Logic.

Appendix A: Göodel Completeness and Incompleteness; Introduction to Computability.

A.1 Revisiting Tarski Semantics.

A.2 Completeness.

A.3 A Brief Theory of Computability.

A.3.1 A Programming Framework for Computable Functions.

A.3.2 Primitive Recursive Functions.

A.3.3 URM Computations.

A.3.4 SemiComputable Relations; Unsolvability.

A.4 Godel's First Incompleteness Theorem.

A.4.1 Supplement: _x(x) " is first order definable in N.

Index.

References 381.