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Topic: If 2 systems represent the same sets do they prove the same theorems?
Replies: 4   Last Post: Feb 3, 2013 11:52 PM

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 Charlie-Boo Posts: 1,635 Registered: 2/27/06
Re: If 2 systems represent the same sets do they prove the same theorems?
Posted: Feb 3, 2013 11:52 PM

On Feb 3, 8:31 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
> On Feb 4, 9:21 am, Charlie-Boo <shymath...@gmail.com> wrote:
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> > On Feb 3, 5:29 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
>
> > > On Feb 2, 3:38 am, Charlie-Boo <shymath...@gmail.com> wrote:
>
> > > > That is, if for every wff w in system A there is a wff v in system B
> > > > such that |-w(x) iff |-v(x) for all x, and likewise for vice-versa B
> > > > is in A, then do systems A and B prove the same theorems?

>
> > > > C-B
>
> > > by extension system A = system B
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> > > However, one system may have restricted comprehension on WFF while the
> > > other does not.

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> > > Herc
>
> > Are you saying yes to my original question?
>
> Your subject line I'm ignoring.
>
> By extension
>
> (ALL(thm)  thm e theoryA <-> thm e theoryB)  <->  (theoryA = theoryB)
>
> ALL(thm) A|-thm   <->  B|-thm
> <->
> A=B
>
> However the set of WFF in each may be different.
>

> The parameter X limits what you are trying to say
> as theorems have higher arity than 1.

X is a tuple where the number of components ranges from zero to
infinity with arbitrary cardinality.

C-B

>
> Herc
> --www.BLoCKPROLOG.com

Date Subject Author
2/3/13 Graham Cooper
2/3/13 Charlie-Boo
2/3/13 Graham Cooper
2/3/13 Charlie-Boo