  The work lays the foundations of the theory of changeable sets. In author
opinion, this theory, in the process of it's development and improvement, can
become one of the tools of solving the sixth Hilbert problem least for physics
of macrocosm.
  From a formal point of view, changeable sets are sets of objects which,
unlike the elements of ordinary (static) sets may be in the process of
continuous transformations, and which may change properties depending on the
point of view on them (the area of observation or reference frame). From the
philosophical and intuitive point of view the changeable sets can look like as
"worlds" in which changes obey arbitrary laws.
