I'm looking to write a dissertation in the field of logic (for a philosophy degree). I'm deeply interested in logic, but whenever I consider the material beyond my courses it becomes pretty daunting. I'm reasonably familiar with: *First Order Logic *Set Theory and ZFC *Cantor's Diagonal Argument *Church/Turing Thesis *Godel / Tarski / Lob limitative results (I find some of this pretty tricky!) *Probability Theory *Utility Theory (Von Neumann / Morgenstern etc.) *Formal Semantics I would really like to talk about infinity / the continuum / aleph-null; but beyond waxing lyrical about how cool they are, I'm not exactly sure what I'd say. I don't know whether I'll end up choosing something too hard. Hopefully this isn't too vague a question. Please spare me the 'do what you feel' and 'you should know for yourself' answers.