I've read several texts that indicate that the anthropic principle (applied to cosmology, and more specifically, to the multiverse) yields the existence of all logically possible universes (most like David Lewis' Modal Realism or Robert Nozick's Principle of Plenitude/Fecundity)
For example, From The Anthropic Cosmological Principle by John Barrow and Frank Tipler (1988):
The question of why does this universe rather than that universe exist is answered by saying that all logically possible universes do exist. What else could there possibly be? The MWI cosmology enlarges the ontology in order to economize on physical laws.
But I have found many texts that contradict this as well.
Firstly, the authors claim that all logically possible worlds exist, but they refer to Everett's MWI (which does not entail every logically possible world, but only those compatible with quantum mechanics).
Secondly, in this paper (http://www.ignaciodarnaude.com/textos_diversos/Multiverse%20scenario.pdf), at page 274, Tipler's multiverse is mentioned
The multiverse argued by Tipler does not involve all logically possible universes, but only those that are consistent with the fundamental laws of physics as we know them today.
This completely contradicts what Tipler and Barrow said in their work.
So, what is happening here? Does Barrow and Tipler's "anthropic multiverse" really propose the existence of all logically possible universes? Do you know of anything these authors wrote or said that indicates that their multiverse really contains all logically possible universes?