Seems like the results in this blog post would be of interest. https://www.scottaaronson.com/blog/?p=2741 https://www.scottaaronson.com/blog/?p=2741 Not so mu

Seems like the results in this blog post would be of interest. https://www.scottaaronson.com/blog/?p=2741 https://www.scottaaronson.com/blog/?p=2741 Not so much in avoiding the halting problem while allowing complexity, but instead using it and actual runnable Turing machines to create ridiculously cool cases of unprovable truths. For example a running Turing machine that only halts if it contradicts set theory.