Evidence and the hierarchy of mathematical theories

It is a well-known fact of mathematical logic, by now developed in considerable detail, that formalized mathematical theories can be ordered by relative interpretability, and the "strength" of a theory is indicated by where it stands in this ordering. Mutual interpretability is an equivalence relation, and what I call an ordering is a partial ordering modulo this equivalence. Of the theories that have been studied, the natural theories belong to a linearly ordered subset of this ordering
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