Imagine you have an oracle that can determine if an arbitrary statement is provable in Peano arithmetic [...] We can’t expect PA to decide whether or not any given Turing machine halts
Imagine you have an oracle that can determine if an arbitrary statement is provable in Peano arithmetic
[...] We can’t expect PA to decide whether or not any given Turing machine halts
The oracle isn’t working in PA, it’s just deciding statements that are in PA.
The oracle isn’t working in PA, it’s just deciding statements that are in PA.