Journal of Symbolic Logic 56 (3):949-963 (1991)

Let $\mathscr{L} = \{0, 1, +, \cdot, <\}$ be the usual first-order language of arithmetic. We show that Peano arithmetic is the least first-order $\mathscr{L}$-theory containing $I\Delta_0 + \exp$ such that every complete extension $T$ of it has a countable model $K$ satisfying. $K$ has no proper elementary substructures, and whenever $L \prec K$ is a countable elementary extension there is $\bar{L} \prec L$ and $\bar{K} \subseteq_\mathrm{e} \bar{L}$ such that $K \prec_{\mathrm{cf}}\bar{K}$. Other model-theoretic conditions similar to and are also discussed and shown to characterize Peano arithmetic.
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DOI 10.2307/2275063
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References found in this work BETA

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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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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