7
votes
Splitting 0' into two 1-generic reals
Let us construct $x$ and $y$ in stages from oracle $0'$, so that they are both $1$-generic, but $x\oplus y$ will code $0'$. We specify the binary digits of $x,y$ in stages. At the first stage, we ...
- 236k
5
votes
Accepted
What's the measure of all 1-generic sets?
It's measure 0. Almost every real is Martin-Löf random, and no random can be 1-generic.
Here's a direct argument, which can also be turned into an argument that no 1-generic is ML-random.
For any $n$...
- 3,073
1
vote
Accepted
Kurtz randomness and supermartingales with infinite *limit*
Assuming you mean a c.e. (super)martingale, this is just Martin-Löf randomness. What needs to be shown is that, for every non-random real, there is a martingale which limit-succeeds on the real. You ...
- 3,073
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