Definition:Forking Extension
Jump to navigation
Jump to search
This article needs to be linked to other articles. In particular: univere, formulas, parameters, sorry should have flagged that as well You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding these links. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{MissingLinks}} from the code. |
Definition
Let $T$ be a complete $\LL$-theory.
Let $\mathfrak C$ be a monster model for $T$.
Let $A\subseteq B$ be subsets of the universe of $\mathfrak C$.
Let $\map p {\bar x}$ be a complete $n$-type over $B$.
Denote by $p \restriction A$ the subset of $p$ consisting of those formulas which involve only parameters from $A$.
$p$ is a forking extension of $p \restriction A$ if and only if $\map p {\bar x}$ forks over $A$.