Non-isomorphic Hyper-real Fields from Non-isomorphic Ultrapowers.
We prove that if ℱ is a non-meager P-filter, then both ℱ and are countable dense homogeneous spaces.
The following statement is proved to be independent from : Let be a Tychonoff space with and . Then a union of less than of nowhere dense subsets of is a union of not greater than of nowhere dense subsets.