Date: Feb 23, 2013 11:20 PM
Author: Zaljohar@gmail.com
Subject: Re: An equivalent of MK-Foundation-Choice
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