Super-rigid families of strongly Blackwell spaces

Droste, Manfred

doi:10.1090/S0002-9939-1988-0947662-2

Super-rigid families of strongly Blackwell spaces
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Proc. Amer. Math. Soc. 103 (1988), 803-808 Request permission

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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