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SUMMARY:Noah Schweber (Proof School)
DTSTART:20210722T180000Z
DTEND:20210722T190000Z
DTSTAMP:20260423T035756Z
UID:OLS/67
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OLS/67/">Cee
 rs higher up</a>\nby Noah Schweber (Proof School) as part of Online logic 
 seminar\n\n\nAbstract\nAbstract: We examine analogues of ceers (computably
  enumerable equivalence relations) in generalized recursion theory - speci
 fically\, in $\\kappa$-recursion theory for $\\kappa$ an uncountable regul
 ar cardinal. Classically\, the degrees of ceers with respect to computable
  embeddability forms a partial order which is maximally complicated\, name
 ly one whose theory is computably isomorphic to that of true arithmetic. W
 e extend this result to the $\\kappa$-ceers. Interestingly\, this requires
  a genuinely new argument\, and currently no single approach is known whic
 h applies both to $\\omega$ and to uncountable regular $\\kappa$. Moreover
 \, the situation for singular cardinals\, let alone admissible ordinals wh
 ich are not cardinals such as $\\omega_1^{CK}$\, is completely open. If ti
 me permits\, we will discuss a second proof of the above result for the sp
 ecial case of $\\kappa=\\omega_1$ which has the advantage of applying to c
 ertain generalized computability theories other than $\\kappa$-recursion t
 heories.\n\nThis is joint work with Uri Andrews\, Steffen Lempp\, and Mana
 t Mustafa.\n
LOCATION:https://researchseminars.org/talk/OLS/67/
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