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SUMMARY:Takayuki Kihara (Nagoya University)
DTSTART:20211005T130000Z
DTEND:20211005T140000Z
DTSTAMP:20260423T005720Z
UID:CTA/69
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CTA/69/">Law
 vere-Tierney topologies for computability theorists</a>\nby Takayuki Kihar
 a (Nagoya University) as part of Computability theory and applications\n\n
 \nAbstract\nIn this talk\, we study the frame of Lawvere-Tierney topologie
 s on Hyland's effective topos. For this purpose\, we introduce a new compu
 tability-theoretic reducibility notion\, which is a common extension of th
 e notions of Turing reducibility and generalized Weihrauch reducibility. B
 ased on the work by Lee and van Oosten\, we utilize this reducibility noti
 on for providing a concrete description of the frame of the Lawvere-Tierne
 y topologies on the effective topos. As an application\, we solve several 
 open problems proposed by Lee and van Oosten. For instance\, we show that 
 there exists no minimal Lawvere-Tierney topology which is strictly above t
 he identity topology on the effective topos.\n
LOCATION:https://researchseminars.org/talk/CTA/69/
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