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first-order and higher-order logic, model theory, set theory, proof theory, computability theory, formal languages, definability, interplay of syntax and semantics, constructive logic, intuitionism, philosophical logic, modal logic, completeness, Gödel incompleteness, decidability, undecidability, theories of truth, truth revision, consistency.
10
votes
Applications of logic to group theory?
One area where logic really helped group theory is the theory of zetafunctions of torsionfree nilpotent groups. Define $\zeta_G(s)=\sum_{U\leq G} (G:U)^{-s}$, where summation runs over all finite inde …
1
vote
undergraduate logic textbook
I gave a course in logic using the lecture notes "Sets, Models and Proofs" by Moerdijk and van Oosten, and the course went quite well. The text is very well written and can be recommended for self-stu …