# Definition:Witness Property

Jump to navigation
Jump to search

## Definition

Let $\LL$ be a language of predicate logic.

Let $\mathscr M$ be a formal semantics for $\LL$.

Let $\FF$ be a set of $\LL$-WFFs.

Suppose that, for every $\LL$-WFF of $1$ free variable $\map \phi x$, if:

- $\FF \models_{\mathscr M} \exists x : \map \phi x$

then there exists some term $t$ containing no variables such that:

- $\FF \models_{\mathscr M} \map \phi {x := t}$

Then, $\FF$ satisfies the **witness property**.

## Sources

This page may be the result of a refactoring operation.As such, the following source works, along with any process flow, will need to be reviewed. When this has been completed, the citation of that source work (if it is appropriate that it stay on this page) is to be placed above this message, into the usual chronological ordering.In particular: This definition is based on Hodges's definition of a Hintikka set, which adds the additional constraint that either $\FF \models_\MM \phi$ or $\FF \models_\MM \neg \phi$ for every $\phi$. I have not managed to obtain a source that uses the term witness property.If you have access to any of these works, then you are invited to review this list, and make any necessary corrections.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 `{{SourceReview}}` from the code. |

- 1993: Wilfrid Hodges:
*Model Theory*