Boolos, Burgess and Jeffrey, 5th edn.
It seems only yesterday that the fourth edition came out: but -- as I
found in the CUP bookshop today --- there's now a fifth edition of
Computability and Logic. The preface announces that the main revision
in this addition is a "simplification of the treatment of the
representability of recursive functions". And the material on Robinson
Arithmetic has been rewritten, and there's a more explicit discussion
of the two uses we can make of Church's Thesis (essential and
eliminable).
I confess to still perhaps preferring the more spartan elegance of the
early editions. And I think that the book has always been, then and
now, rather harder for students than the authors intended (which was
one reason that I imagined that there was room for my G�del book, even
though it criss-crosses over quite a bit of the same territory). But
credit where a great deal of credit is due: this is still a lovely
book, full of good things and with some terrific explanations of
tricky stuff. So hasten to your bookshop ...
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