Karthik Ravishankar

Karthik Ravishankar

I'm a Mathematics PhD student working in Computability Theory.

Talks and presentations

Enumeration Degrees - Local and Global Structure

November 19, 2025

Graduate Student Seminar, University of Illinois Chicago, Chicago, IL, USA

he local structure of the e-degrees refers to the e-degrees below 0’. These correspond precisely to the degrees of the \Sigma_2 sets. We shall talk about enumeration reducibility, its connection to Turing reducibility as well as contrast the local structure of the e-degrees with that of the Turing degrees. After a survey of known results we shall end with our new work and some open questions.

Constrasting the halves of an Ahmad Pair

September 25, 2025

Midwest Computability Seminar XXXV, University of Chicago, Chicago, IL, USA

We study Ahmad pairs in the Σ02 enumeration degrees. We say (A,B) form an Ahmad pair if A ≰e B and every Z <e A satisfies Z ≤e B. Ahmad pairs have recently drawn interest as they are a key obstacle in solving the AE theory of the local structure.

Separating the halves of an Ahmad pair

April 08, 2025

Logic Seminar, University of Wisconsin-Madison, Madison, WI, USA

Incomparable Σ02 sets (A,B) form an Ahmad pair if every set strictly enumeration below A is also enumeration below B. Extending previous work, in this talk we will characterize the left halves of Ahmad pairs as precisely the low3 and join irreducible sets and show that the right halves cannot be low3 thereby giving a natural separation between the two halves. Slides

Characterizing Ahmad pairs in the local structure

November 26, 2024

Logic Seminar, University of Wisconsin-Madison, Madison, WI, USA

A pair (A,B) of Σ2-sets forms an Ahmad pair if every set strictly below A is also below B. We give a characterization for when a set can be the left half of an Ahmad pair. We also introduce a hierarchy of Ahmad n-pairs in the local structure and characterize them using different notions of join irreducibility. The eventual goal is to come up with a property separating the two halves of an Ahmad pair.