Theory of Recursive Functions and Effective Computability

math. If you are an undergraduate and are interested in computability theory, I recommend Nigel's Cutland's book on the subject.


Good reference   June 6, 2000
Peter Gerdes (Los Angelos)
19 out of 20 found this review helpful

I looked long and hard for a reference in recursion theory and this was the only one which was acceptable. Luckily it is also quite good.

Most books in the subject either introduce the material in their own non-standard notation which, while suitable for a survey course in the material is of little help when attempting to actually read papers in the field. These books are also usually very basic ignoring things like the arithmetical hierarchy. Other books in this subject seem to mostly be advanced texts and don't cover, or cover very briefly, the important theorems.

This book starts at turing machines and recursive functions. Going through the basic results like the halting problem and rapidly moving on to more advanced topics like creative sets, cylinders and hypersimple sets. Posts problem(with Friedberg's solution) and the fixed point theorem are covered as well. The final part of the book covers degrees of unsolvability arithmetical hierarchy and the analytic hierarchy.

While the book does cover recursive fucntions and turing machines I would suggest previous experience with them before reading as the coverage is brief and doesn't give the reader a feeling of how these systems work.

If you are taking a class in the subject or want to understand modern recursion theory this is a wonderful place to start.


A Masterpiece   June 27, 2005
Jason T (Canada)
3 out of 3 found this review helpful

If there's a better book on recursive function theory, I havent seen it. It's wonderfully well-written, extremely interesting, and good both for learning and quick reference. There are lots of neat exercises- this book will keep you busy for a long time. If you are interested in recursive function theory you must have this book- I dont need to say anything else.


great book   June 22, 2003
11 out of 11 found this review helpful

There are a lot of good introductory books on computation theory,
but after reading them you may be left asking "okay, what do
I read next?" Well _this_ is the book. If you're looking for something in between the undergraduate intro books and
the research-level articles then this is for you. It develops recursive function theory in a succinct, mathematically mature manner that is freed from the details of any particular formalism. You should have previous exposure to turing machines and undecidable problems, an appreciation of the defense and use of Church's thesis, and familiarity with basic mathematical logic. Just to be clear, this book is NOT:
-a computer science, programming, or algorithms book
-an introductory book
-a book about automata or weak models of computation (such as regular languages or context-free grammars)
-a complexity theory book (no time bounds or np-completeness etc)


Old but still the most popular   July 12, 2005
Nathan Oakes (Ashland, Oregon)
2 out of 3 found this review helpful

After four decades, this is still the most popular graduate text on recursion theory. I think the success is due to its stock of valuable material rather than the quality of writing. The style is dense, descriptions are overly brief, and explanations are poorly laid out. Proofs are brief and sketchy. Overall, it is just poor writing. Take a look at Odifreddi to see recursion theory from someone with a talent for readable prose.

It says no previous logic course is assumed, but you actually need set theory and basic logic from the beginning. Also, coverage of the basics is cursory, so it would help to have done something like Cutland.