Assignments, Tests, and Solutions:
The final exam for this course will be held on Monday, December 9 from 9:00am to 11:30am in Hamilton Hall Room 102. Details will be posted on the course website as they become available.
Lecture # | Date | topics covered | reading/resources/comments |
1 | 04/09/24 | Course introduction, propositional formula | Chapter 2 from textbook |
2 | 05/09/24 | propositional logic syntax and semantics | |
3 | 09/09/24 | truth assignments, Theorem 2.2 | |
4 | 11/09/24 | Theorem 2.2, satisfaction, truth tables, tautologies, logical equivalence | |
5 | 12/09/24 | logical equivalence | |
6 | 16/09/24 | truth functions | |
7 | 18/09/24 | continued. | |
8 | 19/09/24 | logical implication. | |
9 | 23/09/24 | logical implication, continued. | |
10 | 25/09/24 | formal proof system for propositional logic | Chapter 3 |
11 | 26/09/24 | continued, consistency, satisfiability, soundness, completeness | |
12 | 02/10/24 | continued. Compactness Theorem, applications |
|
13 | 03/10/24 | Introduction to first order languages | Chapter 4 |
14 | 07/10/24 | continued | |
15 | 09/10/24 | Structures, interpretation of terms | |
16 | 10/10/24 | satisfaction, examples. | |
17 | 21/10/24 | continued, universally valid formulas | |
18 | 23/10/24 | validity, satisfaction, freely substitutable | |
19 | 24/10/24 | midterm test | |
20 | 28/10/24 | logical equivalence, prenex normal form | |
21 | 30/10/24 | logical implication, axioms, theories, examples, substructures | |
22 | 31/10/24 | substructure, isomorphism | |
23 | 04/11/24 | countable dense linear orders, formal deductive system for first order logic | Chapter 5 |
24 | 06/11/24 | continued, examples, meta-theorems, deduction theorem | |
25 | 07/11/24 | continued | |
26 | 11/11/24 | equality meta-theorem, soundness theorem | |
27 | 13/11/24 | soundness theorem, completeness theorem, normal structures | |
28 | 14/11/24 | continued | |
29 | 18/11/24 | canonical structures, proof of the completeness theorem | |
30 | 20/11/24 | continued | |
31 | 21/11/24 | completeness theorem for uncountable languages, Compactness
theorem |
Chapter 6 |
32 | 25/11/24 | Compactness Theorem, axiomatizability |
|
33 | 27/11/24 | continued, fields |
|
34 | 28/11/24 | Lowenheim-Skolem Theorem |
|
35 | 02/12/24 | continued, models of arithmetic, Skolem's Paradox |
|
36 | 04/12/24 | continued, categoricity |
|
37 | 05/12/24 |