Fickleness and bounding lattices in the recursively enumerable Turing degrees

Abstract: The ability for a recursively enumerable Turing degree $d$ to bound certain important lattices depends on the degree's fickleness. For instance, $d$ bounds $L_7$ (1-3-1) if and only if $d$'s fickleness is $>\omega$ ($\geq\omega^\omega$). We work towards finding a lattice that characterizes the $>\omega^2$ levels of fickleness and seek to understand the challenges faced in finding such a lattice. The candidate lattices considered include those that are generated from three independent points, and upper semilattices that are obtained by removing the meets from important lattices.

logic

Audience: researchers in the topic

Computability theory and applications

Series comments: Description: Computability theory, logic

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