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Re: A compact reformulation of MKFoundationChoice.
Posted:
Mar 22, 2013 5:25 PM


On Mar 19, 12:41 pm, Zuhair <zaljo...@gmail.com> wrote: > This is also another reformulation of MK. > > Define: Set(x) iff Exist y. x in y > > Axioms: > > Unique construction: if phi is a formula in which x is not free, then: > (Exist!x for all y ( y in x iff Set(y) & phi)) is an axiom. > > Pairing: (For all y (y in x > y=a or y=b)) > Set(x) > > Size limitation: Set(x) & y =< H(TC(x)) > Set(y) > > / > > Definitions: > TC(x)={y for all t (x subclass_of t & t is transitive > y in t)} > t is transitive iff for all m,n (m in n & n in t > m in t) > H(x)= {y for all z(z in TC({y}) > z =< x)} > z =< x iff Exist f (f:z >x & f is injective). > / > > This is a more compact presentation of MKFoundationChoice. Which of > course can interpret the whole MK and of course can construct a model > of ZFC thus proving its consistency.
But do you know that your system is consistent? Or if it has a different set of theorems than ZFC (otherwise you are saying that if ZFC is consistent then ZFC is consistent)?
CB
> Zuhair



