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Tagged with independence-results metamathematics
4 questions
8
votes
1
answer
490
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Natural $\Pi_1$ sentence independent of PA
Order invariant graphs and finite incompleteness by Harvey Friedman gives an example of a combinatorial/non-metamathematical $\Pi_1$ sentence that is independent of ZFC. Is there a simpler example of ...
- 2,203
4
votes
2
answers
477
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Experiments physically performable in a finite amount of time whose results are independent of ZFC [closed]
In On independence and large cardinal strength of physical statements we see that their are physical statements which are independent of ZFC, and even strong cardinal axioms. There were many answers, ...
- 6,353
4
votes
2
answers
799
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What things does ZFC not know if it knows?
The statement "ZFC $\vdash 0=1$" is independent of ZFC due to Goedel's second incompleteness theorem. That got me wondering, for what other statements $\phi$ is "ZFC $\vdash \phi$" independent of ZFC?
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- 6,353
7
votes
6
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Formal proof of Con(ZFC) => Con(ZFC + not CH) in ZFC
Is it possible to prove $Con(ZFC) \rightarrow Con(ZFC + \neg CH)$ purely within ZFC? To prove this (using forcing) one seems to need a countable transitive model of ZFC. The texts I am reading avoid ...
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