Models of the Universe

I promised my friend Zoltán a translation of an older post in Spanish, Modelos del Universo, so here it is. It is almost a literal version.

After some reflection on independence proofs in Set Theory using the method of forcing, one of my conclusions was that it should not be too counterintuitive the fact of adding a new set, i.e., a set not obtainable from previous existing ones using the already established operations of set construction.  For instance, we don’t feel any remorse for taking an arbitrary ring $k$ and adjoining an element transcendental over it, obtaining $k[x]$. Continue reading