Re: ZFC


Torkel Franzen wrote:
| Those who say that "we can prove that PA is consistent using ZFC"
|would seem to have no interest whatsoever in any actual consistency
|proof (since it's such absurd overkill to refer to ZFC). It's just
|ritual.

I remember once seeing a paper by Kreisel where he comments
at length on ritualistic tendancies of this kind. If I
remember correctly he attributed some of it to holdovers
from the Hilbert program. People would try to prove a result
in some weak system for no apparent reason, and things like
that.

Keith Ramsay

.

Relevant Pages

  • Re: ZFC
    ... | Those who say that "we can prove that PA is consistent using ZFC" |would seem to have no interest whatsoever in any actual consistency |proof. ... - Ludwig Wittgenstein, Tractatus Logico-Philosophicus. ...
    (comp.theory)
  • Re: THIS STATEMENT HAS NO PROOF IN ANY SYSTEM = true or false?
    ... asking whether the cartesian product of nonempty sets is nonempty. ... If ZF is consistent then there are models of ZF in which AC is false ... things have to be taken in context. ... Let's take "ZFC is consistent" for comparison. ...
    (comp.theory)
  • Re: THIS STATEMENT HAS NO PROOF IN ANY SYSTEM = true or false?
    ... asking whether the cartesian product of nonempty sets is nonempty. ... If ZF is consistent then there are models of ZF in which AC is false ... things have to be taken in context. ... Let's take "ZFC is consistent" for comparison. ...
    (sci.math)
  • Re: THIS STATEMENT HAS NO PROOF IN ANY SYSTEM = true or false?
    ... asking whether the cartesian product of nonempty sets is nonempty. ... If ZF is consistent then there are models of ZF in which AC is false ... things have to be taken in context. ... Let's take "ZFC is consistent" for comparison. ...
    (sci.logic)
  • Re: Rational numbers, irrational numbers: each dense in real numbers
    ... That's all the theorems about those ... inconsistent theorems, then the collection of consistent theorems ... ordinals, to be "the union restricted to i and i is an ordinal", ... ZFC, because there is no universe in ZFC. ...
    (sci.math)