Ceers higher up

Noah Schweber (Proof School)

22-Jul-2021, 18:00-19:00 (4 years ago)

Abstract: Abstract: We examine analogues of ceers (computably enumerable equivalence relations) in generalized recursion theory - specifically, in κ\kappa-recursion theory for κ\kappa 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 κ\kappa-ceers. Interestingly, this requires a genuinely new argument, and currently no single approach is known which applies both to ω\omega and to uncountable regular κ\kappa. Moreover, the situation for singular cardinals, let alone admissible ordinals which are not cardinals such as ω1CK\omega_1^{CK}, is completely open. If time permits, we will discuss a second proof of the above result for the special case of κ=ω1\kappa=\omega_1 which has the advantage of applying to certain generalized computability theories other than κ\kappa-recursion theories.

This is joint work with Uri Andrews, Steffen Lempp, and Manat Mustafa.

logic

Audience: researchers in the topic


Online logic seminar

Series comments: Description: Seminar on all areas of logic

Organizer: Wesley Calvert*
*contact for this listing

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