Plurality of Worlds

I just finished reading Multiverses and blackberries by Martin Gardner (in his 2003 book Are Universes Thicker than Blackberries?). In this article he discusses the Many Worlds Interpretations (MWI) of quantum mechanics. As an extreme example of MWI the work of David Lewis, The Plurality of Worlds (1986, see the wiki page, or read parts on Google books) is mentioned. David Lewis "seriously maintains that every logically possible universe-that is, one with no logical contradictions ... is out there." (M. Gardner, 2003)

It was not the first time I heard about David Lewis' theory, which belongs to modal realism. At first I found it a funny idea: some Universes would be extremely dull because they would exist only of for example of the number 2, others only of 15 - 3 = 12, or of all possible triangles. Others would be rich like ours.

After thinking about it a bit longer, problems arise: all logically consistent Universes have logically consistent histories. Does this mean that every moment in the history of every possible Universe is an Universe? Or is the entire time-line of every possible Universe already there? In the latter case, we would live in an entirely deterministic Universe.

To this moment, I have not read Lewis' work myself, so I cannot be completely certain about the following, but what I know about the Plurality of Worlds-theory suggests a more fundamental problem. A Universe that has no 'parallel Universes' to it, that is the Only One Universe, can be without logical contradictions. According to the theory, that Universe would exist. However, it would rule out all the other Universes.
One may conclude that the Plurality of Worlds-theory itself leads to logical contradictions. The Universes that contain a Plurality of Worlds-theory could therefore not exist within the theory. Since the theory does exist, the Plurality of Worlds-theory must be false!