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abramdemski comments on Reflection in Probabilistic Logic - Less Wrong
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... Or a probability for the continuum hypothesis, axiom of choice, et cetera, if the probabilistic set theory works out. :)
While set theory already does that within forcing language (kinda, truth values are in a boolean algebra instead of a ring) for CH, AC, etc., the values of P!=NP cannot be changed if the models have the same ordinal (due to Shoenfield's absoluteness theorem). I really hope that Probabilistic Set Theory works out, it seems very interesting.