3 ms·
BB(745) is some specific number N. Numbers cannot be independent of ZFC. Only boolean valued formulas can be. In this case, the relevant formula F expresses t
by tromp 3y ago
BB(745) is some specific number N. Numbers cannot be independent of ZFC.
Only boolean valued formulas can be.
In this case, the relevant formula F expresses that all 745 state TMs that do not halt within N steps, will never halt. Assuming consistency of ZFC, formula F is true but unprovable in ZFC, and thus independent.
Another formula G expresses that some specific 745 state TM halts in exactly N steps. Formula G is true and provable in ZFC. F and G together imply that BB(745) = N.