Model-theoretic properties characterizing Peano arithmetic

Journal of Symbolic Logic 56 (3):949-963 (1991)
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Let= {0,1, +,·,<} be the usual first-order language of arithmetic. We show that Peano arithmetic is the least first-order-theory containingIΔ0+ exp such that every complete extensionTof it has a countable modelKsatisfying(i)Khas no proper elementary substructures, and(ii) wheneverL≻Kis a countable elementary extension there isandsuch that.Other model-theoretic conditions similar to (i) and (ii) are also discussed and shown to characterize Peano arithmetic.



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Citations of this work

The Theory of $\kappa$ -like Models of Arithmetic.Richard Kaye - 1995 - Notre Dame Journal of Formal Logic 36 (4):547-559.

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On cofinal extensions of models of fragments of arithmetic.Richard Kaye - 1991 - Notre Dame Journal of Formal Logic 32 (3):399-408.

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