We describe a full nonspurious 4\ensuremath{\Elzxh}\ensuremath{\omega} shell-model calculation that successfully reproduces the low-lying spectrum of $^{16}\mathrm{O}$, including the superdeformed ${0}^{+}$ (6.05 MeV) state, and discuss its connection with the coexistence model. This treatment provides a realistic microscopic framework for discussing various electroweak processes: E2 transitions in $^{16}\mathrm{O}$, the role of exchange currents and the pseudoscalar coupling constant in the ${0}^{+}$\ensuremath{\leftrightarrows}${0}^{\mathrm{\ensuremath{-}}}$ \ensuremath{\beta}-decay and \ensuremath{\mu}-capture transition, and the evaluation of the Gamow-Teller inclusive response function.