A Friendly Introduction to Mathematical Logic
Pearson (Verlag)
978-0-13-010705-3 (ISBN)
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For a one-quarter/one-semester, junior/senior-level course in Mathematical Logic.
With the idea that mathematical logic is absolutely central to mathematics, this tightly focused, elementary text discusses concepts that are used by mathematicians in every branch of the subject—a subject with increasing applications and intrinsic interest. It features an inviting writing style and a mathematical approach with precise statements of theorems and correct proofs. Students are introduced to the main results of mathematical logic—results that are central to the understanding of mathematics as a whole.
1. Structures and Languages.
Naïvely. Languages. Terms and Formulas. Induction. Sentences. Structures. Truth in a Structure. Substitutions and Substitutability. Logical Implication. Summing Up, Looking Ahead.
2. Deductions.
Naïvely. Deductions. The Logical Axioms. Rules of Inference. Soundness. Two Technical Lemmas. Properties of our Deductive System. Non-Logical Axioms. Summing Up, Looking Ahead.
3. Completeness and Compactness.
Naïvely. Completeness. Compactness. Substructures and the Löwenheim-Skolem Theorems. Summing Up, Looking Ahead.
4. Incompleteness—Groundwork.
Introduction. Language, Structure, Axioms of N. Recursive Sets and Recursive Functions. Recursive Sets and Computer Programs. Coding—Naïvely. Coding Is Recursive. Gödel Numbering. Gödel Numbers and N. NUM and SUB Are Recursive. Definitions by Recursion Are Recursive. The Collection of Axioms Is Recursive. Coding Deductions. Summing Up, Looking Ahead. Tables of D-Definitions.
5. The Incompleteness Theorems.
Introduction. The Self-Reference Lemma. The First Incompleteness Theorem. Extensions and Refinements of Incompleteness. Another Proof of Incompleteness. Peano Arithmetic and the Second Incompleteness Theorem. George Boolos on the Second Incompleteness Theorem. Summing Up, Looking Ahead.
Appendix: Set Theory.
Exercises.
| Erscheint lt. Verlag | 12.1.2000 |
|---|---|
| Sprache | englisch |
| Maße | 158 x 235 mm |
| Gewicht | 445 g |
| Themenwelt | Geisteswissenschaften ► Philosophie ► Logik |
| Mathematik / Informatik ► Informatik ► Theorie / Studium | |
| Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre | |
| ISBN-10 | 0-13-010705-0 / 0130107050 |
| ISBN-13 | 978-0-13-010705-3 / 9780130107053 |
| Zustand | Neuware |
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