
Re: An equivalent of MKFoundationChoice
Posted:
Feb 23, 2013 11:20 PM


On Feb 23, 3:16 pm, CharlieBoo <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? > > CB > Look at the title of this post, does it impart the announcement of a "Significant" result? This system is just a reformulation of MKFoundationChoice, 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 MKChoiceFoundation. 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 MKChoiceFoundation. If you have time try enjoying proving it in this system.
Zuhair

