6 citations · 6 across the 6 of their papers we have counts for
4 papers · 1 filter
A Note on a Conjecture of Sacks: It is Harder to Embed Height Three Partial Orders than Height Two Partial Orders
Kojiro Higuchi, Patrick Lutz
A long-standing conjecture of Sacks states that it is provable in ZFC that every locally countable partial order of size continuum embeds into the Turing degrees. We show that this…
Coding information into all infinite subsets of a dense set
Matthew Harrison-Trainor, Lu Liu, Patrick Lutz
Suppose you have an uncomputable set and you want to find a set , all of whose infinite subsets compute . There are several ways to do this, but all of them seem to produ…
Part 1 of Martin's Conjecture for order-preserving and measure-preserving functions
Patrick Lutz, Benjamin Siskind
Martin's Conjecture is a proposed classification of the definable functions on the Turing degrees. It is usually divided into two parts, the first of which classifies functions whi…
The Solecki Dichotomy and the Posner-Robinson Theorem are Almost Equivalent
Patrick Lutz
The Solecki dichotomy in descriptive set theory and the Posner-Robinson theorem in computability theory bear a superficial resemblance to each other and can sometimes be used to pr…