Researching Set Theory as an Undergrad

[mathkid]

I'm currently an undergrad in math who's going to graduate next year. I'm interested in doing research in set theory (not now of course, perhaps in grad school). Unfortunately, I'm at a liberal arts school and there are no set theorists in the math department. All they offer is a naiive set theory course, in fact I'm taking a philosophy course on non classical logic, which is more interesting than what the math department has to offer. I've asked my advisor and other professors at my university and they have no idea about what set theory research entails. So my question is, what do I have to do in order to be able to do research in set theory? I've heard that Jech's text "Set Theory" is a good text for set theory, so I'll probably read that over the summer. How do I prepare for doing research, and what are open problems and theory building to be done. I.e. I don't want to try to do stuff that has already been solved. Given that no one in my math department can answer these questions, it seems like I'll have to try to do the research by myself.

 

[micromass]

Yes, Jech is probably the best text for set theory. But it is also a quite mature text. I would not recommend Jech for a first encounter in set theory. There is also the Hrbacek & Jech book, which is probably better suited for a first encounter: https://www.amazon.com/dp/0824779150/?tag=pfamazon01-20

You might also want to consider reading up on classical logic, more particularly: model theory. That will show up quite a lot in advanced set theory.

 

[mathkid]

Thanks for the advice mathwonk! I don't think I've seen model logic, except in the proof of the nullstellensatz, but I'll look that up for sure. I'll probably read, Hrbacek and Jech's text, and then work my way up to Jech's monster text.