# Is Logic/Set Theory necessary for studying Topos Theory?

I have just completed a postgraduate course, in which I studied Category Theory, without having a background in Set Theory and Logic - this probably already sounds absurd to many. This did not seem to be a problem - at least until now.

As a (reasonable, I thought) progression to my studies, I am trying to teach myself Topos Theory. Until the notion of geometric morphisms, I thought it might be ok to just omit the Logic examples from my studying. And it worked fine, I could keep up with learning. But I have now arrived to the concept of a classifying topos. It feels that now my lack of knowledge in Logic is going to be a very big obstacle. It seems almost impossible to continue. I am worried that this was a big mistake from the beginning. So I am asking the Topos theorists that read this, for their opinion on how stupid they think I have been by thinking in this way, and maybe what is the best way/source to learn what is needed. Thanks for any help.

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I'm hardly a topos theorist. That said, I wouldn't worry too much - when there are several things to be learnt, one has to be first, and the choice may be arbitrary. Have you looked at the text of Moerdijk-MacLane? – Adam Epstein Nov 11 '13 at 8:04
One can definitely omit the logic examples and still get a lot out of the M-M book. However, it might require having an external source of motivation for studying topoi in the first place. – Marguax Nov 11 '13 at 8:23
Thanks for your replies! Of course, it is M-M that I am reading. But I cannot see how lack of knowledge in Logic would allow me to understand the notion of a classifying topos. I mean, the words model and theory have to appear in any definition of a classifying topos... – Muriel Bech Nov 11 '13 at 8:42
@MurielBech, as far as I remember, the book of M-M contains a detailed enough introduction to logic to understand what classifying topoi are. Even if you never had any formal background inlogic, I'm positive that you know what $\forall$, $\exists$ and $\implies$ mean, or how to write statements formally (any basic analysis or algebra course usually explains it). You don't really need more. – Anton Fetisov Nov 11 '13 at 11:14
@Muriel: Don't worry! You haven't been stupid. I did the same thing as you, and I have even taught topos theory as a graduate course. It's very possible to wrap your head around classifying topoi without a formal background in logic, by looking at examples. I would look first at the classifying topos for rings, e.g. That being said, if you choose to learn the logic, you will of course have a deeper understanding, but depending on what you want to do with topos theory, this may not be strictly necessary. – David Carchedi Nov 11 '13 at 11:36