o-minimality variations

[sshresth12]

I wish to attend the logic summer school program by the math department at UCLA. They seem to have an interesting class on o-minimality. However, I have zero knowledge about the same. Can anyone tell me about the prerequisites or concepts I will have to be clear about from before for understanding this class ?
This is the program description on their website :
An infinite totally ordered structure is called o-minimal if every definable set (in one dimension) is a finite union of points and intervals. There is a deep structure theory of definable sets in o-minimal structures, and there are mathematically rich o-minimal structures. In this course, we will develop the theory of o-minimality from the beginning, building up a structure theory of definable sets and providing numerous examples. We will also study variants of o-minimality and applications to differential equations and number theory if time permits.

 

[stapel]

I wish to attend the logic summer school program by the math department at UCLA. They seem to have an interesting class on o-minimality. However, I have zero knowledge about the same. Can anyone tell me about the prerequisites or concepts I will have to be clear about from before for understanding this class ?
This is the program description on their website :
An infinite totally ordered structure is called o-minimal if every definable set (in one dimension) is a finite union of points and intervals. There is a deep structure theory of definable sets in o-minimal structures, and there are mathematically rich o-minimal structures. In this course, we will develop the theory of o-minimality from the beginning, building up a structure theory of definable sets and providing numerous examples. We will also study variants of o-minimality and applications to differential equations and number theory if time permits.

Well, the UCLA page in question states, in part:

Courses are very intensive, and reach advanced material, at a graduate level. They are designed to not require specific background in logic, but they do require high mathematical sophistication, for example from upper division or graduate courses in analysis or algebra. The summer school courses serve as good introduction to the kind of work that students of mathematics can expect in graduate school.

Since the description itself references applications in differential equations and number theory, you'd probably need to be conversant, at the graduate level, with these topics, at the very least. You can review a lecture on the topic here (PDF), and an "introduction" to the topic here (PDF). You can review the compiled "notes" for a course here (PDF). Loads more results are available online (Google). It looks like a solid foundation in abstract algebra would be one of the requirements.

Have fun!