 One possible reaction to these difficulties is to assume that there is a preferred factorization. (One may also regard the above problems as an indication that systems possess their properties in a relational way, see Section 5). The Atomic Modal Interpretation (AMI, Bacciagaluppi and Dickson 1999) thus assumes that nature fixes a set of mutually disjoint atomic quantum systems \(S^j\) that constitute the building blocks of all other quantum systems. From the mathematical point of view, this means that the Hilbert space \(\mathcal{H}^{\univ}\) of the entire universe can only be meaningfully factorized in a single way, which defines a preferred factorization. If each atomic quantum system \(S^j\) corresponds to a Hilbert space \(\mathcal{H}^j\), then the Hilbert space \(\mathcal{H}^{\univ}\) of the universe must be written as