looking for a good reference on Turing degrees and hyperdegrees

From: David Madore (david.madore_at_ens.fr)
Date: 02/23/05 

Date: Wed, 23 Feb 2005 16:00:13 +0000 (UTC)

Hi.

I'm looking for a good reference book (or possibly article) which
would explain clearly and synthetically various known facts about
Turing degrees and hyperdegrees.

I have Roger's *Theory of Recursive Functions and Effective
Computability*, which mostly, but not quite, satisfies my
requirements: the material found there is very much in the line of
what I'm looking for, but it's out of date now and it also has the
annoying tendency of getting too burdened with cumbersome notations.
So, is there a more recent textbook which covers the same kind of
things but going a little further, being a bit more up-to-date and
clearer on the notational side?

To give an idea of what I'm looking fore, here's the sort of thing I
would like to know more about (I'm not really expecting someone to
answer my questions, although that would, of course, be nice :-). If
A is a subset of N, we can define the smallest countable ordinal CK(A)
which is not the order type of a well-ordering of N computable from A
(so CK(0) is the usual Church-Kleene omega_1): what can be said about
the range of the CK? If HJ(A) is the hyperjump of A, is CK(HJ(A)) a
function of CK(A)? Is it perhaps the smallest CK(B) greater than
CK(A)? If not, can we construct such a B? What is the sup of the
CK(A) for A in the analytic hierarchy and how does it compare with the
smallest fixed point of the index function of the range of CK? If
alpha is in the range of CK, is it true that alpha is the inf of CK(A)
for A a well-ordering of N of type alpha? And so on...

Thanks for any pointers! 

-- 
     David A. Madore
    (david.madore@ens.fr,
     http://www.dma.ens.fr/~madore/ )