Re: What is the 1st order formal system known as PA?

Nam Nguyen wrote:
> Rupert wrote:
>
> > Nam Nguyen wrote:
> >
> >>
> >>Let me back tract a little bit and give a slightly different example.
> >>We know ZF and ZFC are 2 *different theories*, yet they both have
> >>the *same binary predicate symbol* "e"! To make the matter worse,
> >>any model of ZFC is one of ZF; and the ZFC theory is effectively also
> >>*a ZF theory*.
> >
> >
> > Why? There are models of ZF that aren't models of ZFC.
>
> There are houses not made of brick, but a brick-house is still
> called a house.
>

Then they're each a "null axiom" theory.

Ross

.

Relevant Pages

  • Re: Subdivisions - US
    ... a developer purchases a large tract of land and divides ... that tract into homesites. ... I mentioned the difference between a tract house and a spec house in ... developers sell the houses before they are built to acquire the ...
    (alt.usage.english)
  • Re: Off to the Long Beach Show
    ... George UT was now one of the top aeas in the US to live. ... Builders just started another tract with starting prices at ... I don't know who can afford houses like that. ...
    (rec.collecting.coins)
  • Re: OT - Plumbing woes
    ... That means ~80% of all houses are less than 60 years old. ... A tract may have 2 or 3 floorplans, ... HVAC/R program for Palm PDA's ... Free demo online at www.pmilligan.net/palm/ ...
    (rec.motorcycles)
  • Re: OT - Plumbing woes
    ... That means ~80% of all houses are less than 60 years old. ... The side walls are the support. ... A tract may have 2 or 3 floorplans, ...
    (rec.motorcycles)
  • Re: OT - Plumbing woes
    ... That means ~80% of all houses are less than 60 years old. ... Old growth lumber is giving way to rapid growth ... poorer quality Douglas fir or pine. ... A tract may have 2 or 3 floorplans, ...
    (rec.motorcycles)