# ${Z}_{2}$

${Z}_{2}$ 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 | ${Z}_{2}$ |
---|---|

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 |