Model-theoretic properties characterizing Peano arithmetic
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AbstractLet = {0,1, +,·,<} be the usual first-order language of arithmetic. We show that Peano arithmetic is the least first-order -theory containing IΔ0 + exp such that every complete extension T of it has a countable model K satisfying(i) K has no proper elementary substructures, and(ii) whenever L ≻ K is a countable elementary extension there is and such that .Other model-theoretic conditions similar to (i) and (ii) are also discussed and shown to characterize Peano arithmetic.
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