# $Z_{2}$

$Z_{2}$ 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.

Title $Z_{2}$ Z2 2013-03-22 12:56:57 2013-03-22 12:56:57 Henry (455) Henry (455) 5 Henry (455) Definition msc 03F35 Z Z2 second order arithmetic