Ceers higher up
Noah Schweber (Proof School)
Abstract: Abstract: We examine analogues of ceers (computably enumerable equivalence relations) in generalized recursion theory - specifically, in -recursion theory for an uncountable regular cardinal. Classically, the degrees of ceers with respect to computable embeddability forms a partial order which is maximally complicated, namely one whose theory is computably isomorphic to that of true arithmetic. We extend this result to the -ceers. Interestingly, this requires a genuinely new argument, and currently no single approach is known which applies both to and to uncountable regular . Moreover, the situation for singular cardinals, let alone admissible ordinals which are not cardinals such as , is completely open. If time permits, we will discuss a second proof of the above result for the special case of which has the advantage of applying to certain generalized computability theories other than -recursion theories.
This is joint work with Uri Andrews, Steffen Lempp, and Manat Mustafa.
logic
Audience: researchers in the topic
Series comments: Description: Seminar on all areas of logic
Organizer: | Wesley Calvert* |
*contact for this listing |