# Definition:Transitive-Closed Class/Linguistic Note

Jump to navigation
Jump to search

## Definition

The term **Transitive-Closed Class** was invented by $\mathsf{Pr} \infty \mathsf{fWiki}$.

As such, it is not generally expected to be seen in this context outside $\mathsf{Pr} \infty \mathsf{fWiki}$.

The concept appears to have been coined by Raymond M. Smullyan and Melvin Fitting under the name **$T$-closed class** in their *Set Theory and the Continuum Problem, revised ed.* of $2010$ for the purpose of an exercise.

It is referred to on $\mathsf{Pr} \infty \mathsf{fWiki}$ as a **transitive-closed class** in order to improve clarity and transparency.

## Sources

- 2010: Raymond M. Smullyan and Melvin Fitting:
*Set Theory and the Continuum Problem*(revised ed.) ... (previous) ... (next): Chapter $5$: Ordinal Numbers: $\S 2$ Ordinals and transitivity: Exercise $2.1$