On 6 Apr., 19:53, Nam Nguyen <namducngu...@shaw.ca> wrote: > On 06/04/2013 11:38 AM, WM wrote: > > > > > > > On 6 Apr., 19:23, Nam Nguyen <namducngu...@shaw.ca> wrote: > > >> In details: > > >> We do have the logical equivalence: > > >> ~Ax[P(x)] <-> Ex[~P(x)] > > >> But we don't have this equivalence: > > >> ~P(SS.....S0) <-> Ex[~P(x)]. > > >> Right? > > > No. Unless SS...S0 is fixed it is the same as x for x in |N. Different > > notation does not make different meaning. > > It was just unclear to you. In my presentation above SS.....S0 is > a _fixed_ constant, _not_ a variable.
Every counterexample of GC, if existing, is a fixed natural number. But I do not pretend that I know such an SS...S0. And that statement with, say 42, does not play a role in my arguing. > ~GC <==> Counter example with a fixed n in |N exists. <==> Fixed n in |N can be found. ==> Goldbach conjecture is decidable.