642 research outputs found
Non-uniformizable sets with countable cross-sections on a given level of the projective hierarchy
We present a model of set theory, in which, for a given , there exists
a non-ROD-uniformizable planar lightface set in , whose all vertical cross-sections are countable sets (and in
fact Vitali classes), while all planar boldface sets with
countable cross-sections are -uniformizable. Thus it is true
in this model, that the ROD-uniformization principle for sets with countable
cross-sections first fails precisely at a given projective level.Comment: A revised version of the originally submitted preprin
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