From Wikipedia
In mathematical logic, a logical theory $T_2$ is a (proof theoretic) conservative extension of a theory $T_1$ if the language of $T_2$ extends the language of $T_1$; every theorem of $T_1$ is a theorem of $T_2$; and any theorem of $T_2$ which is in the language of $T_1$ is already a theorem of $T_1$.
Is a theory, as noted by $T_i$, defined as the set of theorems and axioms of a formal system?
Does a language extending another language means the first language is a superset of the second?
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