Basic Logic 101A Learning Lounge course.
Note: There are many confused or limited introductions to this very interesting subject. And there are many interesting developments in the subject that have been done in the past 50 years or so that change the perspective and relative importance of certain concepts, but which many books and college courses still ignore, speaking in great detail about standard first-order predicate logic and its standard set theoretic model theory, but about nothing else.
Good offline books:
Online resources that are ok:
- Some Stanford Encyclopedia of Philosophy entries: Turing Machines, The Church-Turing Thesis, Curry's Paradox, Russell's Paradox, Principia Mathematica, classical logic, intuitionistic logic, constructive mathematics, automated reasoning.
- Introduction to mathematical logic by K.Podnieks & V.Detlovs. Not bad, but uncompleted and perhaps not extremely pedagogical.
- This anti-platonistic pro-formalistic manifesto, though not the most central text to read, has a bit of information on set theories, Gödel's theorem, model theory etc.: Around Goedel's Theorem.