  The work presents the second part of the second edition of its previous one
published in 2000 under the same title, containing the proof (in ZF) of the
inaccessible cardinals nonexistence, which is enriched and improved now. This
part contains applications of the subinaccessible cardinals apparatus and its
basic tools -- theories of reduced formula spectra and matrices, disseminators
and others, which are used here in this proof and are set forth now in their
more transparent and simplified form. Much attention is devoted to the explicit
and substantial development and cultivation of basic ideas, serving as grounds
for all main constructions and reasonings. The proof of the theorem about
inaccessible cardinals nonexistence is presented in its detailed exposition.
Several easy consequences of this theorem and some well-known results are
presented.
