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.
… 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.