  Set-theoretical, physical, and intuitive notions of continuum are compared.
It is shown that the independence of the continuum hypothesis determines status
and properties of the set of intermediate cardinality. The intermediate set is
a hierarchy of non-equivalent infinite sets. Its description consist of
autonomous theories. In particular, quantum mechanics, classical mechanics, and
geometrical optics should be regarded as components of the complete description
of the intermediate set. The intermediate sets may be produced as a result of a
fission of a continuous interval. The simplest schemes of the fission are
considered. Some analogy with the Standard Model is pointed out.
