should i take this class

cap.r

Hello, I am trying to figure out whether I should take this class but I am not sure if I have the requirements for it. My school has a habit of setting the requirements bar low when the class might actually be difficult and need a lot of prior knowledge on the subject.

It's called Axiomatic set theory.
Development of a system of axiomatic set theory, choice principles, induction principles, ordinal arithmetic including discussion of cancellation laws, divisibility, canonical expansions, cardinal arithmetic including connections with the axiom of choice, Hartog's theorem, Konig's theorem, properties of regular, singular and inaccessible cardinals.

I have never taken a set theory course and am familiar with these topics but am in no way sure of myself. the text being used is Y. Moschovakis, Notes on Set Theory, Second Edition, Springer, 2006.

I have done a few analysis courses and my next one will start with measure theory. I have done some complex analysis with a year of abstract algebra. and a semester of number theory. I am still young as a mathematician and am trying to see if this will be a good addition.

Thanks,
RK

quasar987

Set theory is pretty much in a class of its own, in that unlike the other fields, it does not have repercussions in the other fields. And it's a very difficult field to do research in. Personally, I wouldn't bother taking that class. But read around about set theory and if you feel its something maybe you'd like to study in grad school, then take the class. Otherwise, take something more useful.

letmeknow

Could you expand on this a bit? I like most of the subjects I've encountered so far in a pure masters program (algebra,analysis,topology) and I have studied some set theory also. I have heard that it is hard to publish in this field also, as you said. If one were to study this in a Phd program would the lack of "publishability" affect ones career?

LCKurtz

I would say the answer to your last question is "yes". But that's putting the cart before the horse. I am now retired but I don't recall a single instance in my career where our department was looking for someone with expertise in abstract set theory. Your first problem would be finding a university job if that's what you are looking for.

g_edgar

Tthe question would be do you have experience writing proofs? You say you have taken "analysis courses". Were these courses where you write proofs? If so, then you are probably ready for the set theory course.