Peter M. Gerdes

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math.LO2025

Comparing Notions of Dense Computability on $I ¨ ^{I ¨} $ and $2^{I ¨} $

Peter M. Gerdes

A relatively new topic in computability theory is the study of notions of computation that are robust against mistakes on some kind of small set. However, despite the recent popula…

math.LO2025

The Tree Pulldown Method: McLaughlin's Conjecture and Beyond

Leo A. Harrington, Peter M. Gerdes

This paper finally fully elaborates the tree pulldown method used by one of us (Harrington) to settle McLaughlin's conjecture. This method enables the construction of a computable…

math.LO2024

A $I^_{2}^{0}$ Singleton of Minimal Arithmetic Degree

Peter Gerdes

In the study of the arithmetic degrees (the degree structure induced by relative arithmetic definability, ( $\leq_{a}$ ) the $I ¨ $ -REA sets play a role analogous to the role the r.e.…

Comparing Notions of Dense Computability on I¨I¨ and 2I¨

The Tree Pulldown Method: McLaughlin's Conjecture and Beyond

A I^20​ Singleton of Minimal Arithmetic Degree

Comparing Notions of Dense Computability on $I ¨ ^{I ¨} $ and $2^{I ¨} $

A $I^_{2}^{0}$ Singleton of Minimal Arithmetic Degree