| Class Number |
Date |
Reading |
Brief Description |
| 1 |
Tuesday, 1/26 |
1.1 - 1.5, 2.1 |
Introduction, Countable Sets, Induction and Recursion on the Natural Numbers |
| 2 |
Thursday, 1/28 |
2.2 - 2.5 |
Generating Systems, Freeness, Induction and Recursion |
| 3 |
Tuesday, 2/2 |
2.5, 3.1 - 3.3 |
Generating Expressions and Formulas, Propositional Logic, Semantic Implication |
| 4 |
Thursday, 2/4 |
3.4 - 3.5 |
Syntactic Implication, Soundness and Completeness Theorems |
| 5 |
Tuesday, 2/9 |
3.5 - 3.6 |
Completeness and Compactness Theorems, Applications of Compactness |
| 6 |
Thursday, 2/11 |
4.1 - 4.2 |
First-Order Logic: Terms, Formulas, and Structures |
| 7 |
Tuesday, 2/16 |
4.2 - 4.3 |
Elementary Classes of Structures, Substructures and Homomorphisms |
| 8 |
Thursday, 2/18 |
4.3 - 4.4 |
Substructures and Homomorphisms, Definability |
| 9 |
Tuesday, 2/23 |
4.5 - 4.6 |
Elementary Substructures, Substitution |
| 10 |
Thursday, 2/25 |
5.1 - 5.2 |
Semantic Implication, Theories, Counting Models of a Theory |
| 11 |
Tuesday, 3/1 |
5.2 - 5.4 |
Dense Linear Orderings, Semantic Equivalence, Quantifier Elimination |
| 12 |
Thursday, 3/3 |
5.4 - 5.5 |
Quantifier Elimination, Algebraically Closed Fields |
| 13 |
Tuesday, 3/8 |
6.1 |
Syntactic Implication, Soundness |
| 14 |
Thursday, 3/10 |
6.2 |
The Completeness Theorem |
| 15 |
Tuesday, 3/15 |
6.3 |
Applications of Compactness |
| 16 |
Tuesday, 3/17 |
6.4 |
Random Graphs |
| - |
- |
- |
Spring Break |
| 17 |
Tuesday, 4/5 |
6.5 - 6.6 |
Nonstandard Models of Arithmetic and Analysis |
| 18 |
Thursday, 4/7 |
6.5, 7.1 - 7.3 |
Nonstandard Analysis, Axioms of Set Theory |
| 19 |
Tuesday, 4/12 |
7.3 - 7.5, 8.1 - 8.2 |
Working From the Set Theory Axioms, The Natural Numbers |
| 20 |
Thursday, 4/14 |
8.2 - 8.5 |
The Natural Numbers (Induction and Recursion), Finite Sets, Proper Classes |
| 21 |
Tuesday, 4/19 |
8.6, 9.1 |
Cantor-Schroeder-Bernstein, Power Sets, Well-Orderings |
| 22 |
Thursday, 4/21 |
9.1 - 9.3 |
Well-Orderings, Ordinals, Ordinal Arithmetic |
| 23 |
Tuesday, 4/26 |
9.4 - 9.5 |
Cardinals, Cardinal Arithmetic |
| 24 |
Thursday, 4/28 |
10.1 - 10.2 |
The Axiom of Choice and Equivalents |
| 25 |
Tuesday, 5/3 |
10.3, 11.1 - 11.2 |
Cardinal Exponentiation, Subsets of R, Counting Infinite Models |
| 26 |
Thursday, 5/5 |
11.2 - 11.3 |
Counting Infinite Models, Ultrafilters and Ultraproducts |
| 27 |
Tuesday, 5/10 |
- |
The Set-Theoretic Universe |
| 28 |
Thursday, 5/12 |
- |
Computability and Incompleteness |