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SUMMARY:Brent Cody (Virginia Commonwealth University)
DTSTART:20210326T190000Z
DTEND:20210326T200000Z
DTSTAMP:20260423T024426Z
UID:VCU_ALPS/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VCU_ALPS/3/"
 >Higher indescribability and derived topologies</a>\nby Brent Cody (Virgin
 ia Commonwealth University) as part of VCU ALPS (Analysis\, Logic\, and Ph
 ysics Seminar)\n\n\nAbstract\nThe derived set of a subset of a topological
  space\, also called the Cantor derivative of the set\, is the set of limi
 t points of the set. The concept was introduced by Cantor in 1872 and set 
 theory was initially developed in part to study derived sets on the real l
 ine. Bagaria (2019) introduced the sequence of derived topologies on an or
 dinal $\\delta$\, which are topologies obtained from the interval topology
  on $\\delta$ by declaring certain derived sets to be open. Bagaria used t
 he large cardinal hypothesis of indescribability to show that in some mode
 ls of set theory the first $\\delta$-many derived topologies on $\\delta$ 
 can be non-discrete and furthermore the non-isolated points of these space
 s can be characterized in terms of reflection properties. We will discuss 
 some natural generalizations of Bagaria’s results. For example\, in orde
 r to move beyond the first $\\delta$-many derived topologies on $\\delta$\
 , we introduce diagonal Cantor derivatives and indescribability properties
  that involve certain kinds of infinitely long sentences.\n
LOCATION:https://researchseminars.org/talk/VCU_ALPS/3/
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