Saturated models of peano arithmetic

Journal of Symbolic Logic 47 (3):625-637 (1982)
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We study reducts of Peano arithmetic for which conditions of saturation imply the corresponding conditions for the whole model. It is shown that very weak reducts (like pure order) have such a property for κ-saturation in every κ ≥ ω 1 . In contrast, other reducts do the job for ω and not for $\kappa > \omega_1$ . This solves negatively a conjecture of Chang



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Worlds of Homogeneous Artifacts.Athanassios Tzouvaras - 1995 - Notre Dame Journal of Formal Logic 36 (3):454-474.
Elementary Cuts in Saturated Models of Peano Arithmetic.James H. Schmerl - 2012 - Notre Dame Journal of Formal Logic 53 (1):1-13.
Resplendent models and $${\Sigma_1^1}$$ -definability with an oracle.Andrey Bovykin - 2008 - Archive for Mathematical Logic 47 (6):607-623.

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References found in this work

Model Theory.Michael Makkai, C. C. Chang & H. J. Keisler - 1991 - Journal of Symbolic Logic 56 (3):1096.
Mathematical Logic.J. Donald Monk - 2001 - Bulletin of Symbolic Logic 7 (3):376-376.

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