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  1. Models with second order properties II. Trees with no undefined branches.Saharon Shelah - 1978 - Annals of Mathematical Logic 14 (1):73.
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  • Saturated models of peano arithmetic.J. F. Pabion - 1982 - Journal of Symbolic Logic 47 (3):625-637.
    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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  • On cofinal extensions of models of arithmetic.Henryk Kotlarski - 1983 - Journal of Symbolic Logic 48 (2):253-262.
    We study cofinal extensions of models of arithmetic, in particular we show that some properties near to expandability are preserved under cofinal extensions.
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  • Ultraproducts and Saturated Models.H. Jerome Keisler - 1970 - Journal of Symbolic Logic 35 (4):584-585.
  • Ultraproducts which are not saturated.H. Jerome Keisler - 1967 - Journal of Symbolic Logic 32 (1):23-46.
    In this paper we continue our study, begun in [5], of the connection between ultraproducts and saturated structures. IfDis an ultrafilter over a setI, andis a structure, the ultrapower ofmoduloDis denoted byD-prod. The ultrapower is important because it is a method of constructing structures which are elementarily equivalent to a given structure. Our ultimate aim is to find out what kinds of structure are ultrapowers of. We made a beginning in [5] by proving that, assuming the generalized continuum hypothesis, for (...)
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  • Review: R. MacDowell, E. Specker, Modelle der Arithmetik. [REVIEW]Robert G. Phillips - 1973 - Journal of Symbolic Logic 38 (4):651-652.
  • A mathematical incompleteness in Peano arithmetic.Jeff Paris & Leo Harrington - 1977 - In Jon Barwise & H. Jerome Keisler (eds.), Handbook of Mathematical Logic. North-Holland Pub. Co.. pp. 90--1133.
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