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This tag is for questions about proving that some statement is independent from a theory, meaning it is neither provable nor refutable from that theory. Common examples are the continuum hypothesis from the axioms of ZFC, and the axiom of choice from the axioms of ZF.
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Natural statements independent from true $\Pi^0_2$ sentences
If computability counts, Turing famously showed that if M is a Turing machine equipped with an oracle for the regular halting problem, then M's own halting problem is undecidable by M. And if M2 is a …