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SUMMARY:Philip White (George Washington University)
DTSTART:20221103T180000Z
DTEND:20221103T190000Z
DTSTAMP:20260423T052929Z
UID:OLS/102
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OLS/102/">A 
 Two-Cardinal Ramsey Operator on Ideals</a>\nby Philip White (George Washin
 gton University) as part of Online logic seminar\n\n\nAbstract\nLet $I$ be
  a $\\kappa$-complete ideal on $\\kappa$. Similar to the one-cardinal inef
 fability operator of Baumgartner\, Feng defined a one-cardinal Ramsey oper
 ator on $I$. A basic result of Feng is applying the one cardinal Ramsey op
 erator to $I$ yields a normal ideal. Feng also showed under what condition
 s the ideal given by applying the Ramsey operator is equivalently generate
 d by a “pre-Ramsey” ideal as well as the $\\Pi^1_{n+1}$ indescribabili
 ty ideal.  Finally Feng showed iterated use of the one-cardinal Ramsey ope
 rator forms a proper hierarchy. Feng was able to show these results for $<
  \\kappa+$ iterations of the one-cardinal Ramsey operator by utilizing can
 onical functions. Similar to other results of Brent Cody and the presenter
 \, these results in the one-cardinal setting can be generalized to a two-c
 ardinal setting. The theorems of Feng will be discussed in detail as well 
 as the analogous two-cardinal versions of Brent Cody and the presenter.\n
LOCATION:https://researchseminars.org/talk/OLS/102/
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