  Scales of the microworld are defined on the grounds of the hierarchy that can
be set up within a well ordered finite or infinite countable set of well
ordered sets. Indirect measurements in pure mathematical as well as physical
meaning are considered as the mean to obtain information on the occurring
within each scale. The general concept of the physical laws within a certain
scale is defined in the framework of the set theory. The hypothesis is proposed
that quarks are not within the same scale as other elementary particles are,
but within the following ("smaller", exactly of lower hierarchy) scale. Maybe,
in particular, this is the cause of difficulties of the free quark detection?
Some other consequences of the abovementioned hypothesis are discussed.
  Limitations of the possibility to obtain information on the going on within
sets of low hierarchy (in particular, "small" scales of the microworld, in
physics) and to transfer it toward the set of the highest hierarchy (in
particular, to the macroscopic observer in physics) are found as a consequences
of the multi-step character of measurements. Keywords: microworld scales, set
theory, information value and hierarchy, well-ordered set hierarchy,
sub-quantum physics, indirect measurements, quarks PACS: 02.10.Ab, 03.65.Ta
