That would make the set of axioms a recursive set. A recursively enumerable set is one where the accepting turing machine is not required to stop, or equivalently a set whose elements can be produced one after the other on the tape of a turing machine. --AxelBoldt |
That would make the set of axioms a recursive set. A recursively enumerable set is one where the accepting turing machine is not required to stop, or equivalently a set whose elements can be produced one after the other on the tape of a turing machine. --AxelBoldt The point is that for many purposes recursively enumerable is enough. However the article is wrong as it is now, i.e. its "explanation" of what r.e. is is actually about recursive sets. So maybe we should change the requirements to recursive and add in parentheses that sometimes even r.e. is enough, or something. --AV |
Comments?
As to AxelBoldt's question, you'd have to remind me of what the difference is. The basic idea is that for any wff, a turing machine should be able to determine whether or not that wff is an axiom, the turing machine being guaranteed to halt. -- SJK
That would make the set of axioms a recursive set. A recursively enumerable set is one where the accepting turing machine is not required to stop, or equivalently a set whose elements can be produced one after the other on the tape of a turing machine. --AxelBoldt