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
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. This is joint work with Joe Miller and Mariya Soskova