User:Inthar/Endoparticular extensions

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Goal: Formalize Leri's notion of temp extension naturalness or a some notion that is stronger than Leri!naturalness.

Special case 1

Suppose the base temp tempers out (Sk)^m S(k+1)^n for nonzero integers m and n. An extension by one basis element is natural if it tempers out Sk and S(k+1).