the 8/2(2+2) crowd is almost as annoying as the people who claim that 9.99999... and 10 are different numbers and equally annoying as the people who can't grasp that dividing by zero is as invalid in algebra as it is in arithmetic send tweet
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I think this is a case where being mathematicians, we state something to avoid confusion later, but instead cause even more confusion at the start. We're rather good at that...
Confusion just means I know there's something to learn for me. That's usually good. :) So, when you say these objects are "binary strings", these strings are still potentially infinite in length, and for most of them there's no finite program to generate them, right?
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Exactly. Much of the study is for $\Pi^0_1$ classes, meaning there is some arithmetical function $\phi$, and we are saying $\forall x \, \phi(x)$ is true. After some work, this becomes equivalent to the usual interpretation:
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Some initial segment ('stem') \sigma, and the cone of all its extensions.pic.twitter.com/pyQw10Fv1R
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