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Higher gap morasses, Ia: Gap-two morasses and condensation

Published online by Cambridge University Press:  12 March 2014

Charles Morgan
Charles Morgan*
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, England E-mail: charles.morgan@ucl.ac.uk
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Abstract

This paper concerns the theory of morasses. In the early 1970s Jensen defined (k, α)-morasses for uncountable regular cardinals k and ordinals α < k. In the early 1980s Velleman defined (k, 1)-simplified morasses for all regular cardinals k. He showed that there is a (k, 1)-simplified morass if and only if there is (k, 1)-morass. More recently he defined (k, 2)-simplified morasses and Jensen was able to show that if there is a (k, 2)-morass then there is a (k, 2)-simplified morass.

In this paper we prove the converse of Jensen's result, i.e., that if there is a (k, 2)-simplified morass then there is a (k, 2)-morass.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 63 , Issue 3 , September 1998 , pp. 753 - 787
Copyright
Copyright © Association for Symbolic Logic 1998

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References

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