  Various physical effects resulting from decoherence are discussed in the
algebraic framework. In particular, it is shown that the environment may induce
not only classical properties like superselection rules, pointer states or even
classical behavior of the quantum system, but, what is more, it also allows the
transition from statistical description of infinite quantum systems to quantum
mechanics of systems with a finite number of degrees of freedom. It is shown
that such transition holds for the quantum spin system in the thermodynamic
limit interacting with the phonon field.
