Re: Comparing Proofs of Rosser's 1936 Theorem

Charlie-Boo says...

2. [C-B 2005] If the system is both complete and consistent, then the
refutable sentences coincide with the unprovable sentences, but the
former is an r.e. set whereas the latter is not.

I thought # 2 was shorter, simpler, doesn't involve knowing the proof
that the Halting Problem is unsolvable, and is easier to understand.

Well, why do you believe that the set of unprovable sentences is not
an r.e. set? For proof #2 to be complete, you would have to include
a proof of this lemma.

--
Daryl McCullough
Ithaca, NY

.

Relevant Pages

  • Re: Comparing Proofs of Rossers 1936 Theorem
    ... Charlie-Boo wrote: ... that the Halting Problem is unsolvable, ... why do you believe that the set of unprovable sentences is not ...
    (sci.logic)
  • Re: Comparing Proofs of Rossers 1936 Theorem
    ... Charlie-Boo says... ... refutable sentences coincide with the unprovable sentences, ... that the Halting Problem is unsolvable, ... why do you believe that the set of unprovable sentences is not ...
    (sci.logic)
  • Re: Comparing Proofs of Rossers 1936 Theorem
    ... Daryl McCullough wrote: ... refutable sentences coincide with the unprovable sentences, ... that the Halting Problem is unsolvable, ... why do you believe that the set of unprovable sentences is not ...
    (sci.logic)
  • Re: Comparing Proofs of Rossers 1936 Theorem
    ... Charlie-Boo says... ... Daryl McCullough wrote: ... that the Halting Problem is unsolvable, ... why do you believe that the set of unprovable sentences is not ...
    (sci.logic)
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