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Re: ZFC = only PA (a glorified adding machine) and some arbitrary statements about sets
Posted:
Jun 9, 2013 5:04 AM


On Jun 8, 4:37 pm, Graham Cooper <grahamcoop...@gmail.com> wrote: > On Jun 9, 1:07 am, Peter Percival <peterxperci...@hotmail.com> wrote: > > > CharlieBoo wrote: > > > On Jun 7, 2:24 am, Zeit Geist <tucsond...@me.com> wrote: > > > >> It was actually a desire to assure the consistency of the Calculus > > >> that eventually lead to the creation of ZFC. > > > > You mean avoid Russell's Paradox? > > Just use ALL(F):WFF F<>F > > E(S)A(X) XeS<>X~eX > <> > E(S)A(X) XeS<>X~eX > > E(S)A(X) XeS<>X~eX > <> > E(S)E(S) SeS<>S~eS > > E(S)A(X) XeS<>X~eX > <> > FALSE > > CONTRADICTION CONTAINED IN A SUBFORMULA! > > ~EXIST(RUSSELSET) > > THAT SIMPLE! > > > > > Zermelo created his set theory in order to prove that every set could we > > wellordered. > > PROOF: 0;.44444444544444454444444454454444444544444... > > Herc
Very good  for starters. Now list as many theorems as you can that use the same proof but with different constants, in this case, instead of set and membership. Then identify a theorem that is proven with just one additional step beyond one of these, and apply it to the rest of the theorems. Here's a first step: The set of Turing Machines that do not halt yes on themselves is not recursively enumerable.
CB



