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$Z_2$ (Definition)

$Z_2$ is the full system of second order arithmetic, that is, the full theory of numbers and sets of numbers. It is sufficient for a great deal of mathematics, including much of number theory and analysis.

The axioms defining successor, addition, multiplication, and comparison are the same as those of PA. $Z_2$ adds the full induction axiom and the full comprehension axiom.



"$Z_2$" is owned by Henry.
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Other names:  Z, Z2
Also defines:  second order arithmetic
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Cross-references: comprehension axiom, induction axiom, PA, successor, axioms, analysis, number theory, sufficient, numbers, theory
There are 4 references to this entry.

This is version 2 of $Z_2$, born on 2002-08-17, modified 2006-12-17.
Object id is 3308, canonical name is Z_2.
Accessed 9285 times total.

Classification:
AMS MSC: 03F35 (Mathematical logic and foundations :: Proof theory and constructive mathematics :: Second- and higher-order arithmetic and fragments)
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