Classical Recursion Theory: The Theory of Functions and Sets of Natural Numbers, Vol. 1

I agree with much of what another reviewer has said (July 11, 2005 ). But I don't think that Odifreddi has exaggerated when he claims that the prerequisites of reading his book will be roughly freshman math. Having said that, I admit that since many students in their sophomore year still don't possess a working knowledge of, say proof by mathematical induction, the book is certainly too heavy for those readers. Further aggravating the difficulty for beginners is the book's admittedly less-than-ideal organization and presentation of some portion of the enormously many topics it treats. This will be frustrating for readers who are not enthusiasts of the book's multifarious viewpoints and prefer a quick introduction to the subject instead. I recommend N.Cutland's "Computability" to newcomers. Nevertheless, for those who plan a future career in mathematical logic, especially recursion theory, Odifreddi's book will prove to be a treasure trove of unusual and stimulating insights not easily encountered elsewhere - even though one might not always agree with his ideas. For the future logicians I also recommend R.Soare's "Recursively enumerable sets and degrees" for a deeper treatment of r.e. sets.