Complete set of commuting observables
In quantum mechanics, a complete set of commuting observables (CSCO) is a set of commuting operators whose common eigenvectors can be used as a basis to express any quantum state. In the case of operators with discrete spectra, a CSCO is a set of commuting observables whose simultaneous eigenspaces span the Hilbert space, so that the eigenvectors are uniquely specified by the corresponding sets of eigenvalues.
https://en.wikipedia.org/wiki/Complete_set_of_commuting_observables