 and this in turn is equivalent to the existence of a set of orthogonal projections \(R_{\alpha_1 \ldots\alpha_i}(t_i)\) (for any \(t_i \le t_n\)) that extend consistently the given set of histories and are perfectly correlated with the histories of the original set (Gell-Mann and Hartle 1990). Note, however, that these ‘generalised records’ need not be stored in separate degrees of freedom, such as an environment or measuring  apparatus.[9]