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BEGIN:VEVENT
UID:490ba22480e0bcfd7f00bdc67ac291d1
CATEGORIES:Special Colloquium
CREATED:20211206T100258
SUMMARY:Infinite cardinals and combinatorial principles
LOCATION:Zoom
DESCRIPTION:Abstract: Konig's Lemma states that a countably infinite,finitely branching
  tree has an infinite branch.It is natural to ask whether the analogous res
 ult holds for trees of uncountable height. \nIn 1934, Aronszajn proved that
  this result fails for trees of height $\aleph_1$. On the other hand, this 
 question for trees of height $\kappa \geq \aleph_2$ is intimately connected
  with fundamental questions concerning cardinal arithmetic and the existenc
 e of large cardinals. I will explain this in this talk, and then I will go 
 over recent results about combinatorial principles and cardinal arithmetic.
 \n
X-ALT-DESC;FMTTYPE=text/html:<p>Abstract: Konig's Lemma states that a countably infinite,finitely branch
 ing tree has an infinite branch.It is natural to ask whether the analogous 
 result holds for trees of uncountable height. <br />In 1934, Aronszajn prov
 ed that this result fails for trees of height $\aleph_1$. On the other hand
 , this question for trees of height $\kappa \geq \aleph_2$ is intimately co
 nnected with fundamental questions concerning cardinal arithmetic and the e
 xistence of large cardinals. I will explain this in this talk, and then I w
 ill go over recent results about combinatorial principles and cardinal arit
 hmetic.</p>
CONTACT:Dima Sinapova, University of Illinois at Chicago 
DTSTAMP:20260828T140557
DTSTART;TZID=America/New_York:20211210T130000
DTEND;TZID=America/New_York:20211210T140000
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