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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Just another exposition of MK.
Replies: 10   Last Post: Mar 17, 2013 1:50 PM

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Zaljohar@gmail.com

Posts: 2,632
Registered: 6/29/07
Just another exposition of MK.
Posted: Mar 16, 2013 2:33 AM
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Define: Set(x) iff {x,..}

Extensionality: x C y & y C x -> x=y

Comprehension: {x| Set(x) & phi}

Pairing: x C {a,b} -> Set(x)

Generation: Set(x) & y C H(x) -> Set(y)

where H(x)={z| m in TC({z}). |m| =< |x|}

Size: |x| < |V| -> Set(U(x))

where TC, U stand for transitive closure, union respectively defined
in the customary manner; C is subclass relation; | | =< | | and | | <
| | relations are defined in the standard manner.

The theory above minus axiom of Size is sufficient to prove
consistency of Z. With the axiom of Size it can prove the consistency
of ZF+Global choice, and it is equi-interpretable with MK+Global
choice.

Zuhair

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