Saturated models of peano arithmetic

Journal of Symbolic Logic 47 (3):625-637 (1982)
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Abstract

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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Citations of this work

Atomic saturation of reduced powers.Saharon Shelah - 2021 - Mathematical Logic Quarterly 67 (1):18-42.
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.

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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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