The title of this book is a misnomer, it suggests a work in recursion theory. In fact, this monograph shows how the Z and Vienna develoment method (VDM) specification languages, which are based on set theory, can have computable models. Turner also discusses semantic models that are based on data types, a topic widely covered in other books. (For example, Fitting's text  on the subject is excellent, despite sticking to conventional first-order logic programming.)
The principal contribution of this book is the focus on specification languages rather than programming languages. Unfortunately it lacks historical information and reads like a dry manual. Also, it should have more examples: instead of having just the library database in Chapter 10; in Chapter 18, an event formalism; and in Chapters 18 and 21, a treatment of reals. The examples do not seem very applicable.
Irritatingly, references are repeated at the end of every chapter. There are glaring typographical errors like in the last sentence of Chapter 16.
To avoid buying this longwinded book, read Turner's paper  for a concise treatment of the issues. I also recommend Mitchell's survey  for computable models for various features of type systems.
 Fitting, M.C.
Computability theory, semantics and logic programming.
 Turner, R. The foundations of specification, J. Log. Comput. 15: 623–662, Oct 2005.
 Mitchell, J.C. Type systems for programming languages, in van Leeuwen, J. (ed.) Handbook of theoretical computer science B, North-Holland, 365–458, 1990.