  We introduce a novel set-intersection operator called `most-intersection'
based on the logical quantifier `most', via natural density of countable sets,
to be used in determining the majority characteristic of a given countable
(possibly infinite) collection of systems. The new operator determines, based
on the natural density, the elements which are in `most' sets in a given
collection. This notion allows one to define a majority set-membership
characteristic of an infinite/finite collection with minimal information loss,
compared to the standard intersection operator, when used in statistical
ensembles. We also give some applications of the most-intersection operator in
formal language theory and hypergraphs. The introduction of the
most-intersection operator leads to a large number of applications in pure and
applied mathematics some of which we leave open for further study.
