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Hello, suppose I have a set of sentences Ʃ from the language of number theory ( the usual one ). Then, I extend this to a maximally consistent set of sentences Ʃ' and create a henkin term structure for it ( i.e. as in the popular proof of the completeness theorem ). Can it be true that this resulting structure is isomorphic to the standard structure/model of number theory? Usually, it isn't enough for two structures to satisfy the same sentences for them to be isomorphic, so I am not sure..
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