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  1. Initial Segments of Models of Peano's Axioms.L. A. S. Kirby, J. B. Paris, A. Lachlan, M. Srebrny & A. Zarach - 1983 - Journal of Symbolic Logic 48 (2):482-483.
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  • Model-theoretic properties characterizing Peano arithmetic.Richard Kaye - 1991 - Journal of Symbolic Logic 56 (3):949-963.
    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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  • Models with Orderings.H. J. Keisler, B. van Rootselaar & J. F. Staal - 1974 - Journal of Symbolic Logic 39 (2):334-335.
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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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