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Abstract and Applied Analysis
Volume 2014, Article ID 184071, 11 pages
Research Article

Isomorphic Universality and the Number of Pairwise Nonisomorphic Models in the Class of Banach Spaces

School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK

Received 7 December 2013; Revised 22 March 2014; Accepted 30 March 2014; Published 20 May 2014

Academic Editor: S. A. Mohiuddine

Copyright © 2014 Mirna Džamonja. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We develop the framework of natural spaces to study isomorphic embeddings of Banach spaces. We then use it to show that a sufficient failure of the generalized continuum hypothesis implies that the universality number of Banach spaces of a given density under a certain kind of positive embedding (very positive embedding) is high. An example of a very positive embedding is a positive onto embedding between and for 0-dimensional and such that the following requirement holds for all and in : if , then there are constants and with and .