Extensional Language Property

languages

Definition

Extensional Language Property

A language property $P$ is extensional iff it depends only on the language itself.

Equivalently: if two Turing machines $M_1,M_2$ satisfy

$$L(M_1)=L(M_2)⟹P(L(M_1))=P(L(M_2))$$

This is the “semantics vs. syntax” separation used by Rice.