# Sandwich Principle/Linguistic Note

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## Linguistic Note on Sandwich Principle

The name **Sandwich Principle** for this lemma appears to have been coined by Raymond M. Smullyan and Melvin Fitting in their *Set Theory and the Continuum Problem, revised ed.*.

As they explain, when $x \subset y \subset z$, we may consider $y$ to be **sandwiched** between $x$ and $z$.

Thus the **Sandwich Principle** tells us that, given the conditions constraining $x$, $y$ and $\map g x$, there can be no such $y$ **sandwiched** between $x$ and $\map g x$.

## Sources

- 2010: Raymond M. Smullyan and Melvin Fitting:
*Set Theory and the Continuum Problem*(revised ed.) ... (previous) ... (next): Chapter $3$: The Natural Numbers: $\S 4$ A double induction principle and its applications: Lemma $4.9$: Remarks