We present a model based on the gauge symmetry that relates the mass hierarchy of the fermions with the solution to the strong problem through the Peccei-Quinn symmetry. This last symmetry arises accidentally with the imposition of a discrete symmetry, which also secludes the different scales in the double seesaw mechanism taking place in the neutrino sector. The symmetry breakdown is performed by three scalar triplets plus a scalar singlet hosting an axion field, whose particle excitation can be a component of dark matter. We show a mechanism where a small effective vacuum expectation value is generated for a scalar triplet which is supposed to have a bare mass above the energy scale where the symmetry is broken. Combined with the energy scale in which the is broken, such a mechanism gives rise to a natural hierarchy to the fermions. Beyond the Standard Model particle content, the model predicts an invisible axion, , three GeV neutrinos, , plus several new particles at the TeV scale which are: five vector bosons, , , , and ; one up-type , and two down-type quarks; and at least a -even, , plus non-Hermitian neutral, , , scalar bosons. The model may be tested by looking for the possible production of such particles at the LHC.