## You are here

Homeinterpolation property

## Primary tabs

# interpolation property

A logic is said to have the *interpolation property* if whenever $\phi(R,S)\rightarrow\psi(R,T)$ holds, then there is a sentence $\theta(R)$, so that both $\phi(R,S)\rightarrow\theta(R)$ and $\theta(R)\rightarrow\psi(R,T)$ hold, where $R,S$ and $T$ are some sets of symbols that occur in the formulas, $R$ being the set of symbols common to both $\phi$ and $\psi$.

The interpolation property holds for first order logic. The interpolation property is related to Beth definability property and Robinson’s consistency property. Also, a natural generalisation is the concept $\Delta$-closed logic.

Defines:

interpolation property

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

03B99*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff
- Corrections