Some consequences of TD and sTD.

Liang Yu (Nanjing University)

03-Jun-2021, 01:00-02:30 (3 years ago)

Abstract: TD says that for every cofinal set $A$ of \emph{Turing degrees}, $A$ contains an upper cone; and sTD says that for every set $A$ of \emph{reals} with cofinal range in the Turing degrees, $A$ has a pointed subset (a pointed set is a perfect set in which every real computes a representation of the set). We prove some consequences of TD and sTD. For example, we prove that sTD implies for every set of reals, its Hausdorff dimension can be approximated by it closed subsets.

logic

Audience: researchers in the topic


Computability theory and applications

Series comments: Description: Computability theory, logic

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