Michael Sipser’s Introduction to the Theory of Computation goes over the recursion theorem and Rice’s theorem, IIRC. The proofs are given as well as associated exercises. The textbook walks you through, from DFAs to Turing Machines, so it’s pretty self-contained, if you’re looking at a source other than Computability and Logic to understand them.
Michael Sipser’s Introduction to the Theory of Computation goes over the recursion theorem and Rice’s theorem, IIRC. The proofs are given as well as associated exercises. The textbook walks you through, from DFAs to Turing Machines, so it’s pretty self-contained, if you’re looking at a source other than Computability and Logic to understand them.