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

logic

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)?

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.