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Re: An equivalent of MKFoundationChoice
Posted:
Feb 23, 2013 7:16 AM


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
> The following theory is equal to MKFoundationChoice > > Language: FOL(=,e) > > Define: Set(x) iff Ey. x e y > > Axioms: ID axioms+ > > 1.Extensionality: (Az. z e x <> z e y) > x=y > > 2. Construction: if phi is a formula in which x is not free, > then (ExAy.y e x<>Set(y)&phi) is an axiom > > 3. Pairing: (Ay. y e x > y=a or y=b) > Set(x) > > 4. Size limitation > Set(x) <> Ey. y is set sized & Azex(Emey(z<<m)) > > where y is set sized iff Es. Set(s) & y =< s > and z<<m iff z =<m & AneTC(z).n =<m > > TC(z) stands for 'transitive closure of z' defined in the usual manner > as the minimal transitive class having z as subclass of; transitive of > course defined as a class having all its members as subsets of it. > > y =< s iff Exist f. f:y>s & f is injective. > > / > > Of course this theory PROVES the consistency of ZFC. > Proofs had all been worked up in detail. It is an enjoying experience > to try figure them out. > > Zuhair



