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THE HANF NUMBER FOR AMALGAMATION OF COLORING CLASSES
Published online by Cambridge University Press: 29 June 2016
Abstract
We study amalgamation properties in a family of abstract elementary classes that we call coloring classes. The family includes the examples previously studied in [3]. We establish that the amalgamation property is equivalent to the disjoint amalgamation property in all coloring classes; find the Hanf number for the amalgamation property for coloring classes; and improve the results of [3] by showing, in ZFC, that the (disjoint) amalgamation property for classes Kα studied in that paper must hold up to ℶα (only a consistency result was previously known).
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- Copyright © The Association for Symbolic Logic 2016
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