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

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  • Mirna Džamonja

Abstract

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 .

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  • Mirna Džamonja, 2014. "Isomorphic Universality and the Number of Pairwise Nonisomorphic Models in the Class of Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-11, May.
    • Handle: RePEc:hin:jnlaaa:184071
    DOI: 10.1155/2014/184071
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