It seems to me that you can't have a "prime" predicate in your language. As soon as you add it, the meaning of prime changes (I'm not sure this predicate how adding would work in the models: would the model-checking involve an algorithm for primality-checking? That sounds too complex.). I imagine you can get a Feferman-hierarchy sort of thing, where you're adding predicates instead of axioms, i.e. we have a never-ending chain, in which model equivalence classes are getting finer.
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krja
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Date: 2007-05-02 03:26 pm (UTC)It seems to me that you can't have a "prime" predicate in your language. As soon as you add it, the meaning of prime changes (I'm not sure this predicate how adding would work in the models: would the model-checking involve an algorithm for primality-checking? That sounds too complex.). I imagine you can get a Feferman-hierarchy sort of thing, where you're adding predicates instead of axioms, i.e. we have a never-ending chain, in which model equivalence classes are getting finer.