We will live stream the local logic seminar with the following login information:
Zoom link to local UW logic seminar
Meeting ID: 986 3594 0882
On alternate Mondays, we will join the biweekly virtual Midwest Computability Seminar (a joint seminar of the University of Wisconsin-Madison, the University of Chicago and the University of Notre Dame), with the following login information:
Zoom link to Midwest Computability Seminar
Meeting ID: 997 5433 2165
Some of us will be watching the Midwest Computability Seminar in room B115 Van Vleck, so feel free to join us in person or remotely.
Kihara, Ng, and Pauly have studied various classes that arise from different spaces. They show that any enumeration degree is contained in a class arising from some computable, submetrizable space, and that no T1-space contains all enumeration degrees. Similarly, they separate T2-classes from T1-classes, and T2.5-classes from T2-classes. We give separations of the T2.5-classes from the submetrizable classes using the Arens co-d-CEA degrees and the Roy halfgraph above degrees.
We will continue in this direction showing (non)reductions between problems related to the Cantor-Bendixson theorem with particular attention paid to classifying them for every computable Polish space X. This leads us to the result that, while PKX and wCBX (i.e., same as PKX but where the output also provides a listing of the elements in the scattered part) are equivalent for any space X that we consider, the problem CBX (i.e., same as wCBX but where the output provides also the cardinality of the scattered part) "almost" splits into two Weihrauch degrees, one having as representative PKX and the other having CBNN.
This is joint work with Alberto Marcone and Manlio Valenti.
We present a new result toward showing the decidability by proving that no so-called Ahmad triple can exist. At the end, we will sketch how this proof can be obtained by varying a direct proof of Ahmad (1990) that there is no symmetric Ahmad pair; on the other hand, we also show that our result cannot be strengthened to so-called weak Ahmad triples.