# Beth property

A logic is said to have the *Beth property* if whenever a predicate^{} $R$ is implicitly definable by $\varphi $ (i.e. if all models have at most one unique extension^{} satisfying $\varphi $), then $R$ is explicitly definable relative to $\varphi $ (i.e. there is a $\psi $ not containing $R$,such that $\varphi \vDash \forall {x}_{1},..,{x}_{n}(R({x}_{1},\mathrm{\dots},{x}_{n})\leftrightarrow \psi ({x}_{1},\mathrm{\dots},{x}_{n}))$).

Title | Beth property |
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Canonical name | BethProperty |

Date of creation | 2013-03-22 13:49:40 |

Last modified on | 2013-03-22 13:49:40 |

Owner | Aatu (2569) |

Last modified by | Aatu (2569) |

Numerical id | 7 |

Author | Aatu (2569) |

Entry type | Definition |

Classification | msc 03B99 |

Defines | Beth property |

Defines | Beth definability property |