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Universal structures in power ℵ1
Journal of Symbolic Logic 55 (2):466-477 (1990)
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.My notes
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Citations of this work
The descriptive set-theoretical complexity of the embeddability relation on models of large size.Luca Motto Ros - 2013 - Annals of Pure and Applied Logic 164 (12):1454-1492.
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.
References found in this work
Almost-disjoint sets the dense set problem and the partition calculus.James E. Baumgartner - 1976 - Annals of Mathematical Logic 9 (4):401-439.
On universal graphs without instances of CH.Saharon Shelah - 1984 - Annals of Pure and Applied Logic 26 (1):75-87.
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