Science involves descriptions of the world we live in. It also
depends on nature exhibiting what we can best describe as a high
aLgorithmic content. The theme running through this collection of
papers is that of the interaction between descriptions, in the form
of formal theories, and the algorithmic content of what is
described, namely of the modeLs of those theories. This appears
most explicitly here in a number of valuable, and substantial,
contributions to what has until recently been known as 'recursive
model theory' - an area in which researchers from the former Soviet
Union (in particular Novosibirsk) have been pre-eminent. There are
also articles concerned with the computability of aspects of
familiar mathematical structures, and - a return to the sort of
basic underlying questions considered by Alan Turing in the early
days of the subject - an article giving a new perspective on
computability in the real world. And, of course, there are also
articles concerned with the classical theory of computability,
including the first widely available survey of work on
quasi-reducibility. The contributors, all internationally
recognised experts in their fields, have been associated with the
three-year INTAS-RFBR Research Project "Com putability and Models"
(Project No. 972-139), and most have participated in one or more of
the various international workshops (in Novosibirsk, Heidelberg and
Almaty) and otherresearch activities of the network.
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