Z2 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 theoryMathworldPlanetmathPlanetmath and analysis.

The axioms defining successorMathworldPlanetmathPlanetmathPlanetmath, additionPlanetmathPlanetmath, multiplication, and comparison are the same as those of PA. Z2 adds the full induction axiomMathworldPlanetmath and the full comprehension axiom.

Title Z2
Canonical name Z2
Date of creation 2013-03-22 12:56:57
Last modified on 2013-03-22 12:56:57
Owner Henry (455)
Last modified by Henry (455)
Numerical id 5
Author Henry (455)
Entry type Definition
Classification msc 03F35
Synonym Z
Synonym Z2
Defines second order arithmetic