Lu Liu

collaborators

3 papers

math.LO2016

Generalized low solution of $RT_{k}^{1}$ problem

Lu Liu

We study the "coding power" of an arbitrary $RT_{k}^{1}$ -instance. We prove that every $RT_{k}^{1}$ -instance admit non trivial generalized low solution. This is somewhat…

math.LO2016

$RT_{2}^{2}$ does not imply $WKL_{0}$

Lu Liu

We prove that $RCA_{0} + RT_{2}^{2} \neq \to WKL_{0}$ by showing that for any set $C$ not of PA-degree and any set $A$ , there exists an infinite subset $G$ o…

math.LO2016

Cone avoiding closed sets

Lu Liu

We prove that for an arbitrary subtree $T$ of $2^{< ω}$ with each element extendable to a path, a given countable class $M$ closed under disjoint union, and any set $A$ , i…

Generalized low solution of RTk1​ problem

RT22​ does not imply WKL0​

Cone avoiding closed sets

Generalized low solution of $RT_{k}^{1}$ problem

$RT_{2}^{2}$ does not imply $WKL_{0}$