Re: Continuum hypothesis



I wrote:
You're asking, if I parse the question correctly, whether the set of
statements P such that every statement A undecidable in ZFC+P has the
property that it is conservative over ZFC+P for arithmetical
statements is recursively enumerable. The answer is that this set,
being empty, is trivially recursively enumerable.

A correction: the set is empty if we require ZFC+P to be consistent,
and the set of sentences P such that P is refutable in ZFC otherwise.
Both are r.e. of course.

--
Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)

"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus

.



Relevant Pages

  • Re: Small Set theory:Revised.
    ... Ax.5: Axiom of choice. ... Universe: Ev Ay. ... Let a be a set that is not empty. ... If this theory is consistent it should be something more than ZFC, ...
    (sci.math)
  • Re: The empty set
    ... where phi is a stratified formula denotes a set. ... i.e. 0 is empty. ... Since in ZFC, all variables can only instantiate to sets, ... urelement. ...
    (sci.logic)
  • Re: was: Definition of ordinal exponentiation
    ... > finitely-supported functions from b to a, ... whether "the empty function" (the one whose domain is empty and ... There is necessarily a prior philosophical question about whether ... In the ZFC framework this can all be ...
    (sci.logic)
  • Re: The empty set
    ... Huh?! ... Hence 0 is the set containing all empty sets, ... Since in ZFC, all variables can only instantiate to sets, ... to amount to the use of 'unrestricted comprehension'. ...
    (sci.logic)
  • Re: Aleph_Aleph_1
    ... in ZFC. ... "Wovon man nicht sprechen kann, darüber muss man schweigen" ...
    (sci.logic)

Quantcast