What does it mean for a theory T' to be a conservative extension of a theory T in the same subject area?
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Get StartedWhat does it mean for a theory T' to be a conservative extension of a theory T in the same subject area?
Options:
- T' adds new symbols or axioms but proves no new sentences in the original language of T
- T' extends T and proves strictly more sentences in T's original language
- T' only adds new constant symbols but no axioms
- T' changes the interpretation of existing symbols so old theorems may fail
Correct answer: T' adds new symbols or axioms but proves no new sentences in the original language of T
Explanation: A conservative extension adds new symbols/axioms while preserving provability of formulas in the original language; mechanism: no new old-language sentences become derivable.
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