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 |