The incompleteness phenomenon : a new course in mathematical logic /
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| Author / Creator: | Goldstern, Martin. |
|---|---|
| Imprint: | Wellesley, Mass. : A K Peters, c1995. |
| Description: | xiii, 247 p. : ill. ; 24 cm. |
| Language: | English |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/2331435 |
Table of Contents:
- 1. The Framework of Logic. 1.1. Induction. 1.2. Sentential Logic. 1.3. First Order Logic. 1.4. Proof Systems
- 2. Completeness. 2.1. Enumerability. 2.2. The Completeness Theorem. 2.3. Nonstandard Models of Arithmetic
- 3. Model Theory. 3.1. Elementary Substructures and Chains. 3.2. Ultraproducts and Compactness. 3.3. Types and Countable Models
- 4. The Incompleteness Theorem. 4.1. The Language of Peano Arithmetic. 4.2. The Axioms of Peano Arithmetic. 4.3. Basic Theorems of Number Theory in PA. 4.4. Encoding Finite Sequences of Numbers. 4.5. Godel Numbers. 4.6. Substitution. 4.7. The Incompleteness Theorem. 4.8. Other Axiom Systems. 4.9. Bounded Formulas. 4.10. A Finer Analysis of 4.4 and 4.5. 4.11. More on Recursive Sets and Functions.