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THE HANF NUMBER FOR AMALGAMATION OF COLORING CLASSES

Published online by Cambridge University Press:  29 June 2016

ALEXEI KOLESNIKOV
Affiliation:
DEPARTMENT OF MATHEMATICS TOWSON UNIVERSITY 8000 YORK RD., TOWSON MD 21252, USA E-mail: akolesnikov@towson.edu
CHRIS LAMBIE-HANSON
Affiliation:
EINSTEIN INSTITUTE OF MATHEMATICS GIVAT RAM CAMPUS HEBREW UNIVERSITY OF JERUSALEM JERUSALEM 91904, ISRAEL E-mail: clambiehanson@math.huji.ac.il

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 K α studied in that paper must hold up to α (only a consistency result was previously known).

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Copyright
Copyright © The Association for Symbolic Logic 2016 

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References

Baldwin, J., Categoricity, vol. 50, American Mathematical Society, Providence, RI, 2009.Google Scholar
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