# consistent

If $T$ is a theory of $\mathcal{L}$ then it is consistent iff there is some model $\mathcal{M}$ of $\mathcal{L}$ such that $\mathcal{M}\models T$. If a theory is not consistent then it is inconsistent.

A slightly different definition is sometimes used, that $T$ is consistent iff $T\u22a2\u0338\perp $ (that is, as long as it does not prove a contradiction^{}). As long as the proof calculus used is sound and complete^{}, these two definitions are equivalent^{}.

Title | consistent |
---|---|

Canonical name | Consistent |

Date of creation | 2013-03-22 13:00:20 |

Last modified on | 2013-03-22 13:00:20 |

Owner | Henry (455) |

Last modified by | Henry (455) |

Numerical id | 6 |

Author | Henry (455) |

Entry type | Definition |

Classification | msc 03B99 |

Defines | inconsistent |