Adopting a new universal algebraic approach, this book explores and
consolidates the link between Tarski's classical theory of
equidecomposability types monoids, abstract measure theory (in the
spirit of Hans Dobbertin's work on monoid-valued measures on
Boolean algebras) and the nonstable K-theory of rings. This is done
via the study of a monoid invariant, defined on Boolean inverse
semigroups, called the type monoid. The new techniques contrast
with the currently available topological approaches. Many positive
results, but also many counterexamples, are provided.
General
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