Tegmark postulates in his hypothesis that all possible mathematical structures would exist. But does he include also possible mathematical structures described by other types of logic like paraconsistent logic?
Wikipedia describes paraconsistent logic as follows:
A paraconsistent logic is a logical system that attempts to deal with contradictions in a discriminating way. Alternatively, paraconsistent logic is the subfield of logic that is concerned with studying and developing paraconsistent (or "inconsistency-tolerant") systems of logic.
Max Tegmark has four levels to his multiverse hierarchy. However all of these levels include possible worlds. They do not contain contradictions. He writes: (first page of pdf)
...the key point to remember is that parallel universes are not a theory, but a prediction of certain theories. For a theory to be falsifiable, we need not be able to observe and test all its predictions, merely at least one of them.
Since a contradiction would falsify the prediction of the underlying theories supporting these multiverses, these universes would not contain contradictory observations. At most the logics available in such universes would, like our own, provide a way to "deal with contradictions in a discriminating way".
Tegmark, M. (2009). The multiverse hierarchy. arXiv preprint arXiv:0905.1283. Retrieved on May 14, 2019 from arXiv.org at https://arxiv.org/pdf/0905.1283.pdf
Wikipedia contributors. (2019, April 6). Paraconsistent logic. In Wikipedia, The Free Encyclopedia. Retrieved 18:57, May 14, 2019, from https://en.wikipedia.org/w/index.php?title=Paraconsistent_logic&oldid=891268995