I was inspired to ask this question after watching Joel David Hamkins give a talk about natural instances of non-linearity in consistency strength. Basically, large cardinal axioms seems to be linearly ordered in consistency strength. However, it is known, as a purely formal matter, that the hierarchy of consistency strength is non-linear. The statements used to demonstrate non-linearity are thought of as unnatural. So, that raises the question, what is the formal definition of a natural instance of non-linearity in consistency strength?
2026-03-30 10:42:31.1774867351
What is the formal definition of a natural instance of non-linearity in consistency strength?
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