  In a recent article, M. Tegmark poses the hypothesis that our known universe
is a ``baggage free'' mathematical structure among many other possible ones,
which also correspond to other physical universes --Mathematical Universe
Hypothesis, MUH. Naturally, questions arise, such as how to obtain the physical
properties of our world from the mathematical structure, or how many
possibilities exist for a Universe minimally similar to ours.
  In this letter we present some results which can be regarded as a
strengthening of MUH, as they give some hints on the derivation of spacetime in
current physics from a baggage free mathematical structure.
  Concretely, we argue that the set of mathematical structures which can be
interpreted as a description of a spacetime is drastically reduced, if one
admits some natural postulates on minimal symmetry. Furthermore, the apparently
very particular form of classical Galilei-Newton and relativistic spacetimes,
is not arbitrary and cannot be regarded as ``two possibilities among
arbitrarily many others''. In fact, such theories are determined by a single
mathematical structure which only permits four possible types of spacetimes.
Finally, we show how the minimal postulates on symmetry can be endowed with a
simple physical interpretation, i.e., they acquire ``baggage'' in a natural
way.
