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. adds the full induction axiom
and the full comprehension axiom.
Title | |
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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 |