Universal structures in power ℵ1

Journal of Symbolic Logic 55 (2):466-477 (1990)
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Abstract

It is consistent with ¬CH that every universal theory of relational structures with the joint embedding property and amalgamation for P --diagrams has a universal model of cardinality ℵ 1. For classes with amalgamation for P --diagrams it is consistent that $2^{\aleph_0} > \aleph_2$ and there is a universal model of cardinality ℵ 2.

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10.2307/2274640

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Citations of this work

Universal graphs and functions on ω1.Saharon Shelah & Juris Steprāns - 2021 - Annals of Pure and Applied Logic 172 (8):102986.
On the existence of universal models.Mirna Džamonja & Saharon Shelah - 2004 - Archive for Mathematical Logic 43 (7):901-936.
Morasses, square and forcing axioms.Charles Morgan - 1996 - Annals of Pure and Applied Logic 80 (2):139-163.

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On universal graphs without instances of CH.Saharon Shelah - 1984 - Annals of Pure and Applied Logic 26 (1):75-87.

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