Continuous model theory and its applications

Math 712

The class will meet Tuesdays from 12:30 - 2:30 in HH 410 beginning Sept. 11. The course will roughly follow the outline below. Students will be responsible for producing detailed lecture notes for this course - this will be the basis for the grade. The actual division of labour will be determined once we know who is in the course. In addition, each student will make a presentation on a topic of their choice related to the course material. Slides, reference material and other relevant links will appear on this page.

Math 712

The class will meet Tuesdays from 12:30 - 2:30 in HH 410 beginning Sept. 11. The course will roughly follow the outline below. Students will be responsible for producing detailed lecture notes for this course - this will be the basis for the grade. The actual division of labour will be determined once we know who is in the course. In addition, each student will make a presentation on a topic of their choice related to the course material. Slides, reference material and other relevant links will appear on this page.

Course Outline

Week 1 - Sept. 11: Introduction - why model theory?; ultraproducts and metric structures - Slides for lecture 1

I will not follow the notes of Ben Ya'acov et al in detail but they will provide another treatment of the same material.

Week 2 - Sept. 18: Compactness and the Henkin construction - Slides for lecture 2

Week 3 - Sept. 25: Topology, types and definable sets - Slides for lecture 3

Week 4 - Oct. 2: More definable sets and omitting types - Slides for lecture 4

Week 5 - Oct. 9: Quantifier elimination; basic examples - Slides for lecture 5

Week 6 - Oct. 16: Ehrenfeucht-Fraisse games; more illustrative examples - Slides for lecture 6

Week 7 - Oct. 23: Saturated and atomic models, imaginaries - Slides for lecture 7

Week 8 - Oct. 30: More imaginaries; conceptual completeness - Slides for lecture 8

Week 9 - Nov. 6: Introduction to stability - Slides for lecture 9

Other relevant material can be found in Ben Ya'acov's paper with Usvyatsov and my paper with Farah and Sherman.

Week 10 - Nov. 13: More stability; characterization of independence - Slides for lecture 10

You can find other relevant material in Casanovas' paper (it is a 2007 publication entitled "Simplicity simplified") and in Adler's thesis.

Week 11 - Nov. 20: More stability - slides for lecture 11

Week 12 - Nov. 27: Applications to operator algebras - C*-algebras and von Neumann algebras - slides for lecture 12

Week 13 - Dec. 11: More on operator algebras - slides for lecture 13

I will not follow the notes of Ben Ya'acov et al in detail but they will provide another treatment of the same material.

Week 2 - Sept. 18: Compactness and the Henkin construction - Slides for lecture 2

Week 3 - Sept. 25: Topology, types and definable sets - Slides for lecture 3

Week 4 - Oct. 2: More definable sets and omitting types - Slides for lecture 4

Week 5 - Oct. 9: Quantifier elimination; basic examples - Slides for lecture 5

Week 6 - Oct. 16: Ehrenfeucht-Fraisse games; more illustrative examples - Slides for lecture 6

Week 7 - Oct. 23: Saturated and atomic models, imaginaries - Slides for lecture 7

Week 8 - Oct. 30: More imaginaries; conceptual completeness - Slides for lecture 8

Week 9 - Nov. 6: Introduction to stability - Slides for lecture 9

Other relevant material can be found in Ben Ya'acov's paper with Usvyatsov and my paper with Farah and Sherman.

Week 10 - Nov. 13: More stability; characterization of independence - Slides for lecture 10

You can find other relevant material in Casanovas' paper (it is a 2007 publication entitled "Simplicity simplified") and in Adler's thesis.

Week 11 - Nov. 20: More stability - slides for lecture 11

Week 12 - Nov. 27: Applications to operator algebras - C*-algebras and von Neumann algebras - slides for lecture 12

Week 13 - Dec. 11: More on operator algebras - slides for lecture 13