Math 144: Model Theory and Algebra (Fall 2013)

Monday, Wednesday, Friday 11 am - 12 pm

Faculty:	Nate Ackerman	TA:	---
E-mail:	nate AT math.harvard.edu

This is the approximate schedule of what should be covered in class with the associated reading.

Week	Date	Reading
1	September 4, 2013 September 6, 2013	Introduction and History Languages and Structures: Section 1.1
2	September 9, 2013 September 11, 2013 September 13, 2013	Theories: Section 1.2 Definable Sets: Section 1.3 Definable Sets M^eq Definable Sets: Section 1.3 Interpretations Interpret Complex number in Reals
3	September 16, 2013 September 18, 2013 September 20, 2013	Compactness Theorem: Section 2.1 Compactness/Completeness Non-standard models of arithmetic/set theory Henkin constructions Complete Theories: Section 2.2 Categoricity implies complete Algebraicly Closed Fields Vector Spaces Equivalence Relations with properties
4	September 23, 2013 September 25, 2013 September 27, 2013	Complete Theories: Section 2.2 Injective polynomials from C^n to C^n Elementary Chains Lowenheim-Skolem Theorems: Section 2.3 Upwards Elementary Embedding
5	September 30, 2013 October 2, 2013 October 4, 2013	Lowenheim-Skolem Theorems: Section 2.3 Downwards Skolem Functions Back and Forth: Section 2.4 Linear Orders Random Graph 0-1 Laws EF Games Scott's Isomorphism Theorem Potential Isomorphism
6	October 7, 2013 October 9, 2013 October 11, 2013	Quantifier Elimination: Section 3.1 Dense Linear Orders Divisible Abelian Groups Presburg Arithmetic Model Completeness Model Completions Algebraically Closed Fields: Section 3.2 Zariski Closed and Constructable Sets Hilbert's Basis Theorem Elimination of Imaginaries
7	October 16, 2013 October 18, 2013	Types: Section 4.1 Definitions/Basic Results Stone Spaces Examples Dense Linear Orders Algebraicly Closed Fields Omitting Types and Prime Models: Section 4.2 Omitting Types Theorem
8	October 21, 2013 October 23, 2013 October 25, 2013	Omitting Types and Prime Models: Section 4.2 Prime and atomic models Countable homogeneous models Prime Model Extensions of omega-Stable Theories Saturated and Homogeneous Models : Section 4.3 Countably Saturated Models Existence of Saturated Models
9	October 28, 2013 October 30, 2013 November 1, 2013	Ultrapowers Ultrafilters Existence Arrow's Impossibility Theorem Ultraproducts Saturation Compactness of Topological Spaces Monster model Saturated and Homogeneous Models: Section 4.3 Homogeneous and Universal Models Applications of Saturated Models Vaught's Two Cardinal Theorem Number of Countable Models: Section 4.4 aleph_0-Categorical Models
10	November 4, 2013 November 6, 2013 November 8, 2013	Partition Theorems: Section 5.1 Ramsey's Theorem Connections to combinatorics Indiscernibles: Section 5.2 Ehrenfeucht-Mostowski Models Indiscernibles in Stable Theories Applications of Erdos-Rado
11	November 11, 2013 November 13, 2013 November 15, 2013	A Many-Models Theorem: Section 5.3 Uncountably Categorical Theories: Section 6.1
12	November 18, 2013 November 20, 2013 November 22, 2013	Uncountably Categorical Theories: Section 6.1 Strongly Minimal Sets Existence of Strongly Minimal Formulas The Categoricity Theorem Morley Rank: Section 6.2 Morley Rank Monster Model
13	November 25, 2013	Morley Rank: Section 6.2 Morley Degree Ranks of Types Strongly Minimal Theories Morley Rank in Strongly Minimal Theories Morely Rank in Algebraically Closed Fields
14	December 2, 2013 December 4, 2013	Final Project Presentations

This page was created by Nate Ackerman, and last revised on August 3, 2013.