sentences:  In this copy, all the usual mathematical concepts can be defined, and the 'sets' (in reality, the 'formula_1-sets') turn out to be those q-sets whose transitive closure contains no m-atoms.In formula_1 there may exist q-sets, called "pure" q-sets, whose elements are all m-atoms, and the axiomatics of formula_1 provides the grounds for saying that nothing in formula_1 distinguishes the elements of a pure q-set from one another, for certain pure q-sets.Within the theory, the idea that there is more than one entity in "x" is expressed by an axiom which states that the quasi-cardinal of the power quasi-set of "x" has quasi-cardinal 2qc("x"), where qc("x") is the quasi-cardinal of "x" (which is a cardinal obtained in the 'copy' of ZFU just mentioned).