Upcoming Events

Logic Colloquium

November 07, 2025, 4:10 PM

60 Evans Hall

Mariya Soskova
University of Wisconsin-Madison

The jump and the skip in the enumeration degrees

Enumeration reducibility is a positive reducibility between sets of natural numbers. They were introduced through attempts to extend Turing reducibility to partial functions in a meaningful way. We say that X is enumeration reducible to Y if every enumeration of Y computes an enumeration of X. The Turing degrees embed into the enumeration degrees as the total degrees. There are two known ways to extend the jump operator from the total degrees to all enumeration degrees: Cooper introduced the enumeration jump in 1984, while more recently, in 2019 Andrews et al. introduced the skip operator. I will discuss how these operators interact, I will describe some of their structural properties and survey directions of work in this area where we have exciting open questions including definability, decidability and questions arising from Martin’s conjecture in the Turing degrees.

Logic Colloquium

November 21, 2025, 4:10 PM

60 Evans Hall

Douglas Blue
University of Pittsburgh

Logic Colloquium

December 05, 2025, 4:10 PM

60 Evans Hall

Obrad Kasum
UCLA