Winter 2018: Model theory and o-minimal structures
- Jesse pointed out that there was something missing from the proof of Lemma 2.4 in O-minimal structures: I applied Exercise 2.2 as if formulated for definable subsets of arbitrary finite powers of $M$, which it wasn’t. The notes are now corrected.
- Please save unfinished posts as Drafts. Only choose “submit for review” once you are ready to submit your assignment; this makes it easier for me to see whether you are still working on it or not.
Homework and suggested problems
| Due date | Problem | Remarks |
| Jan 12 | Give a detailed proof of Proposition 1.8 in Structures | discussion only |
| Jan 19 | Homework 1 | hand in |
| Jan 26 | Homework 2 | hand in |
| Feb 13 | Homework 3 | hand in |
| Mar 2 | Homework 4 | hand in |
| Mar 9 | Exercises 1.5, 1.7 and 1.9 in Expansions of dense linear orders Exercises 2.2 in O-minimal structures |
hand in |
| Mar 16 | Exercise 3.3 in Monotonicity Exercise 4.4 in Definable closure Exercises 5.2 in Cell decomposition |
hand in |
| Mar 23 | Exercise 5.13 in Cell decomposition | hand in |
Covered so far
| Tuesday | Friday | |
| Jan 04–05 | Structures | |
| Jan 08–12 | Morphisms | Theories |
| Jan 15–19 | Vaught’s Test | Quantifier elimination |
| Jan 22–26 | Application to algebraically closed fields | Real closed fields Van den Dries’s notes on real closed fields |
| Jan 29–Feb 02 | aster.ca/~speisseg/blog/wordpress/wp-content/uploads/2018/01/quantifier_elimination.pdf”>Application to real closed fields | class cancelled |
| Feb 05–09 | Model completeness | Types (Saturation) (Omitting types) |
| Feb 12–16 | Algebraic closure | Pregeometries (Strong minimality) |
| Feb 26–Mar 02 | Expansions of dense linear orders | O-minimal structures |
| Mar 05–09 | Monotonicity | Definable closure Cell decomposition |
| Mar 12–16 | Cell decomposition | Cell decomposition |
| Mar 19–23 | Dimension | Dimension O-minimal expansions of groups |
General information
| Instructor: | Patrick Speissegger |
| Office: | HH 409A |
| Telephone: | extension 23430 |
| E-mail: | speisseg at math dot mcmaster dot ca |
| Office Hours: | By appointment. |
| Lectures: | Tuesday 11–12:15 in HH/410 and Friday 10–11:15 in HH/207. |
| Course notes: | posted under “Covered so far” |
| Recommended reading: | Model theory, by David Marker, Springer Verlag, 2002; Graduate Texts in Mathematics 217. Tame topology and o-minimal structures, by Lou van den Dries, Cambridge University Press, 1998; LMS Lecture Notes Series 248. Geometric categories and o-minimal structures, by Lou van den Dries and Chris Miller, Duke Math. J. 84, Number 2, 1996, pp. 497–540. |
| Assessment: | Your grade will be based on in-class participation (20%) and submitted solutions to suggested problems (80%). |
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