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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Super-rigid families of strongly Blackwell spaces


Author: Manfred Droste
Journal: Proc. Amer. Math. Soc. 103 (1988), 803-808
MSC: Primary 28A20; Secondary 28A05, 54C05, 60A99
DOI: https://doi.org/10.1090/S0002-9939-1988-0947662-2
MathSciNet review: 947662
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Abstract: We construct a complete subfield $ F$ of $ P({\mathbf{R}})$, isomorphic to $ P({\mathbf{R}})$, of pairwise non-Borel-isomorphic rigid strong Blackwell subsets of $ {\mathbf{R}}$ such that there are only 'very few' measurable functions between any two members of $ F$. As a consequence, we obtain large chains and antichains of non-isomorphic rigid strong Blackwell subsets of $ {\mathbf{R}}$. Also, there is a collection of continuously many dense subsets of $ {\mathbf{R}}$ such that any two of them differ only by two elements, but none of them is a continuous image of any other.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0947662-2
Keywords: Blackwell space, strong Blackwell space, rigid Borel space, separable space, measurable function
Article copyright: © Copyright 1988 American Mathematical Society