Correlation structure can be introduced into the shell model by means of a product of pair correlation functions, each of which vanishes within the repulsive core radius and then approaches unity with a short range dependent only on the Fermi momentum and the relative energy of the pair. Correlations of this type are independent of the state of a particule within a given shell-model orbit. The additional effect of such scalar, state-independent correlations on the magnetic moment of a "closed shell plus one" nucleus is shown to vanish, leaving only the shell-model value. The proof can be extended to correlations having a scalar spin dependence and to certain more complicated symmetries. The effect of residual state-dependent correlations due to terms in the relative momentum of the correlated pair and to the space-exchange part of the attraction as it appears in the correlations is estimated for O17 as a correction to the magnetic moment of 0.002 magneton. There is no modification to the magnetic moment operator due to velocity dependence of the correlation functions, and the expectation value of the ordinary space exchange operator coming from the exchange part of the Hamiltonian is shown to be the same as given by the shell model.