Introduction to mathematical logic - A problem solving course
  This is a set of 288 questions written for a Moore-style course in Mathematical Logic. I have used these (or some variation) four times in a beginning graduate course. Topics covered are:   propositional logic   axioms of ZFC   wellorderings and equivalents of AC   ordinal and cardinal arithmetic   first order logic, and the compactness theorem   Lowenheim-Skolem theorems   Turing machines, Church's Thesis   completeness theorem and first incompleteness theorem   undecidable theories   second incompleteness theorem 
Arnold W. Miller