Karthik Ravishankar

Karthik Ravishankar

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

Posts by Collection

portfolio

publications

talks

Characterizing Ahmad pairs in the local structure

Published:

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.

Separating the halves of an Ahmad pair

Published:

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

Download Slides

Constrasting the halves of an Ahmad Pair

Published:

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.

Enumeration Degrees - Local and Global Structure

Published:

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.

teaching

Grading Duties

UW-Madison

Grader for graduate logic classes MATH770 (Foundations of Math), MATH771 (Set Theory), MATH773 (Computability Theory) and undergraduate classes MATH522 (Analysis 2), MATH475 (Intro Combinatorics), MATH567 (Modern Number Theory)