Math 444

Senior Seminar: Mathematical Logic

General Information Schedule Homework

Schedule

Class Number Date Reading Brief Description
1 Tuesday, 1/25 1.1 - 1.5, 2.1 Introduction, Countable Sets, Induction and Recursion on the Natural Numbers
2 Thursday, 1/27 2.2 - 2.5 Generating Systems, Freeness, Induction and Recursion
3 Tuesday, 2/1 2.5, 3.1 - 3.3 Generating Expressions and Formulas, Propositional Logic, Truth Assignments, Connectives
4 Thursday, 2/3 3.4 - 3.6 Semantic and Syntactic Implication, Soundness Theorem
5 Tuesday, 2/8 3.6 - 3.7 Completeness and Compactness Theorems, Applications of Compactness
6 Thursday, 2/10 4.1 - 4.2 First-Order Logic: Terms, Formulas, Structures
7 Tuesday, 2/15 4.3 - 4.5 Definability, Substitution, Semantic Equivalence
8 Thursday, 2/17 5.1 - 5.2 Elementary Classes, Substructures and Homomorphisms
9 Tuesday, 2/22 5.3 - 5.4 Definability and Automorphisms, Counting Models
10 Thursday, 2/24 5.5 - 6.1 Elementary Substructures, Semantic Implication
- Tuesday, 3/1 - No Class
11 Thursday, 3/3 6.1 - 6.3 Semantic and Syntactic Impliction, Soundness and Completeness Theorems
12 Tuesday, 3/8 6.3 - 6.4 Completeness and Compactness Theorems
13 Thursday, 3/10 6.5 - 6.6 Theories, Random Graphs
14 Tuesday, 3/15 7.1 - 7.2 Diagrams, Embeddings, Nonstandard Models
15 Thursday, 3/17 7.2 Nonstandard Models of Arithmetic and Analysis
- - - Spring Break
16 Tuesday, 4/5 7.3 - 7.4 Universal Sentences, Quantifier Elimination
17 Thursday, 4/7 7.4 - 7.5 Quantifier Elimination, Algebraically Closed Fields
18 Tuesday, 4/12 11.1 - 11.2 Primitive Recursive Functions and Relations
19 Thursday, 4/14 11.2 - 11.3 Coding Primitive Recursive Funcions, Partial Recursive Functions
20 Tuesday, 4/19 11.4 - 11.5 A Machine Model of Computation, The Church-Turing Thesis
21 Thursday, 4/21 11.5 - 11.6 Computably Enumerable Sets
22 Tuesday, 4/26 12.1 Coding Formulas and Deductions, Decidable and Axiomatizable Theories
23 Thursday, 4/28 12.2 Definability in Arithmetic
24 Tuesday, 5/3 12.3 The First Incompleteness Theorem
25 Thursday, 5/5 8.1 - 8.2, 8.7 Axiomatic Set Theory
26 Tuesday, 5/10 - Presentations
27 Thursday, 5/12 - Presentations