```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 meansthat the axiomshere proves all axioms of that theory and vise verse. By the way thisconnotations youare giving to the word 'result' is not always associated with it, forexample in many articlesit is said "side result", insignificant result, etc..., here I alreadysaid a "cute" result whichmeans not significant but nice in some ways. The axiom of sizelimitation here provesUnion, Power, Infinity, Separation and Replacement which is a niceresult. It does thatusing a natural relation that is 'subnumerous' and also the hereditaryconcept usingtransitive closures is not far from the essentials of set concept.What this axiomis saying is that a class is a set iff there is a set sized class thathereditarily bound it.Details of hereditary bounding is in the axiom. This is a rathersimple notion and seeingthe resulting theory PROVING all axioms of MK-Choice-Foundation. is anice non trivialresult albeit not that significant since we didn't come up withsomething new at the end, it isjust MK-Choice-Foundation. If you have time try enjoying proving it inthis system.Zuhair
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