# Beth property

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

Title Beth property BethProperty 2013-03-22 13:49:40 2013-03-22 13:49:40 Aatu (2569) Aatu (2569) 7 Aatu (2569) Definition msc 03B99 Beth property Beth definability property