[Math] Model Theory, Proof Theory, Set Theory, Recursion Theory: Where to begin


What comes after an introduction to Mathematical Logic? Also, Where would Formal Language Theory stand among the other four branches of Mathematical Logic (listed in the title)?

Best Answer

It depends on what your goals are. If you have a basic introduction to logic (e.g. Enderton's book or the book by Boolos, Burgess, and Jeffrey), you have the background to learn significant amounts of each of the four areas.

One thing most general introductions to logic lack is a solid background in basic set theory, particularly ordinals and cardinals. A nice book like Halmos' Naive Set Theory (undergraduate level) or the first couple chapters of Kunen's Set Theory (graduate level) will remedy that. In particular, you need to be relatively comfortable with ordinal and cardinal arithmetic, proofs by transfinite induction, and with the distinction between $2^{\omega}$ vs. $\omega_1$, in order to digest many mid-level results in model theory and proof theory.