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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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Re: If 2 systems represent the same sets do they prove the same theorems?
Posted:
Feb 3, 2013 11:52 PM
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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:
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> > > On Feb 2, 3:38 am, Charlie-Boo <shymath...@gmail.com> wrote:
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> > > > 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?
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> > > > C-B
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> > > 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
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> > Are you saying yes to my original question?
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> Your subject line I'm ignoring.
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> By extension
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> (ALL(thm) thm e theoryA <-> thm e theoryB) <-> (theoryA = theoryB)
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> ALL(thm) A|-thm <-> B|-thm
> <->
> A=B
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> However the set of WFF in each may be different.
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> 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
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