You don't need to search. You are correct that PM is one approach to avoiding the paradox. — TonesInDeepFreeze
I do not believe there is a set of all sets either in Russell's type theory or in any version of modern type theory. I'd be grateful if you could supply references and/or context to the contrary. — fishfry
Why would I want to supply references to a claim that PM allows a set of all sets when I agree that PM does not allow a set of all sets? — TonesInDeepFreeze
You are correct that PM is one approach to avoiding the paradox. — TonesInDeepFreeze
It is correct that PM is one approach to avoiding the paradox. With PM there is no set of all sets. — TonesInDeepFreeze
I was talking about type theory in general avoiding the issue of the set of all sets by assigning hierarchy types as I last read about the issue. — Shawn
Yes, sir. — Shawn
No, I addressed exactly the sentence he wrote. What he wrote in that sentence was correct. I am not responsible for addressing other confusions he has that might conflict with the sentence he posted and to which I responded. He wrote something correct, and I affirmed it. — TonesInDeepFreeze
Do you think complexity class can determine "complexity" quantifiably for a Turing computable algorithm? — Shawn
Rather, it's about know the complexity of solving this particular solvable problem. — TonesInDeepFreeze
A machine for ascertaining the length of the shortest proof of a theorem doesn't involve anything like oracles. — TonesInDeepFreeze
OK, I sat down, read it, and read it more, and seemingly you would have the have a powerful oracle machine to make the decision to do this with least decidedly complexity.
Am I getting that much right? — Shawn
how does the machine do this without a brute force method? — Shawn
The method I mentioned is brute force. I don't know whether there's a better method. — TonesInDeepFreeze
How would you define it? Is it even possible to define this? And, may I ask how is this distinct from estimating Kolmogorov complexity? — Shawn
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