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Topic: How simple Z is?
Replies: 1   Last Post: Apr 23, 2013 11:10 PM

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Posts: 2,665
Registered: 6/29/07
How simple Z is?
Posted: Apr 23, 2013 3:23 PM
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Pre-Z is the closure of all of what is provable from the logical
axioms of first order logic and the following axioms by the rules of
inference of first order logic (Hilbert style).

Comprehension: if phi is a formula then a set {x C A| phi} exists.

Infinity: Exist N. 0 in N & for all m. m in N -> {m} in N.


where C is the known "subset" relation.

It is nice to know that Pre-Z interpets Z. And that MOST of
mathematics can be formalized within it (through its interpretation of
Z of course).


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