Talks - Spring 2019

Title

Speaker

Date

Time

Venue

Abstract

A weak-2 generic that bounds a minimal degree

Prof. Satyadev Nandakumar

31st January 2019

5:00-6:00 PM

KD102

The downward density of a class of Turing degrees is the following property: given two Turing degrees a and b from that class such that a is less than b, there is a Turing degree c of that class such that a is less than c and c is less than b? If the class of sets computes a minimal degree, then density does not hold. In 1980, Carl Jokusch showed that the class of sufficiently generic sets is dense by establishing that 2-generics are downward dense below a given 2-generic. In 1990 Kumabe, and independently, Chong and Downey established that 1-generics are not dense, by constructing a minimal degree computable from a 1-generic. For a well-studied intermediate notion, weakly 2-generics, the density question was open. We settle the question by showing that there is a minimal degree computable from a weakly 2-generic. The proof uses a technique from recursion theory called full approximation. (This is joint work with Rod Downey.)

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Sumanta Ghosh

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Rajendra Kumar

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Mahesh S R

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