This is pretty standard model theory: the class of models of the total theory is empty (viceversa: the theory of the class of all models is empty).
I’m not sure why level IV would restrict itself to standard model theory. In a tri-valued logic (i.e., all propositions are either true, false, or both), there are non-trivial models of trivialism.
I’m not sure why level IV would restrict itself to standard model theory. In a tri-valued logic (i.e., all propositions are either true, false, or both), there are non-trivial models of trivialism.
Trivialism would not respect Tegmark IV’s subsections which comply with our model of logic.