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Jul 10, 2015 at 9:46 comment added Emil Jeřábek What do you mean by a "suitable interpretation" of $P$? For any theory $T$, there are predicates that preserve all properties of the theory (e.g., the empty predicate), and there are predicates that destroy all nice properties (e.g., an elementhood predicate satisfying ZFC). (And, of course, for most niceness properties except elimination of imaginaries and the like, adding a predicate can never make the theory nicer than it already was.)
Jul 9, 2015 at 19:43 history asked Darío G CC BY-SA 3.0