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Re: An equivalent of MK-Foundation-Choice
Posted:
Feb 23, 2013 11:20 PM
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On Feb 23, 3:16 pm, Charlie-Boo <shymath...@gmail.com> wrote:
> On Feb 20, 6:01 pm, Zuhair <zaljo...@gmail.com> wrote:
> > This is just a cute result.
>
> Is that an attempt to brag in the context of being modest but not
> really by calling it cute?
>
> just = only = modest
> &
> cute = nothing significant, just looks like a precious little baby
> but
> result = new discovery in the history of mathematics = very
> significant
>
> Which is it - modesty or delusions of grandeur?
>
> C-B
>
Look at the title of this post, does it impart the announcement of a
"Significant" result?
This system is just a reformulation of MK-Foundation-Choice, it means
that the axioms
here proves all axioms of that theory and vise verse. By the way this
connotations you
are giving to the word 'result' is not always associated with it, for
example in many articles
it is said "side result", insignificant result, etc..., here I already
said a "cute" result which
means not significant but nice in some ways. The axiom of size
limitation here proves
Union, Power, Infinity, Separation and Replacement which is a nice
result. It does that
using a natural relation that is 'subnumerous' and also the hereditary
concept using
transitive closures is not far from the essentials of set concept.
What this axiom
is saying is that a class is a set iff there is a set sized class that
hereditarily bound it.
Details of hereditary bounding is in the axiom. This is a rather
simple notion and seeing
the resulting theory PROVING all axioms of MK-Choice-Foundation. is a
nice non trivial
result albeit not that significant since we didn't come up with
something new at the end, it is
just MK-Choice-Foundation. If you have time try enjoying proving it in
this system.
Zuhair
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