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Results tagged with independence-results
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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.
10
votes
Arithmetic statement which is independent, and whose independence is independent, and so on?
If $p$ is independent of ZFC, and ZFC is sound, then $I(p)$ is independent of ZFC.
Indeed, because ZFC is sound, it can't disprove $I(p)$ because $I(p)$ is true.
However, $I(p)$ implies consistency of …
- 148k
3
votes
Experiments physically performable in a finite amount of time whose results are independent ...
Based on our current partial understanding of the laws of physics, it does appear that, to the extent to which the results of physical experiments are governed by mathematical theories that we underst …
- 148k