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UID:20250701T064546EDT-5313vOC3Fv@132.216.98.100
DTSTAMP:20250701T104546Z
DESCRIPTION:Title: Monsters\, Forcing Axioms\, and (no) large cardinals\n	Ab
 stract\n	As we all know\, in consequence of the Axiom of Choice many so-cal
 led 'monstrous' sets exist\, such as Hamel bases\, a subset of the plane w
 hich meets every line in exactly two points\, MAD families\, and so on... 
 For many of these sets\, it is known that they must be complicated\, in th
 e sense that their construction cannot proceed in few\, simple\, effective
  steps (this can be made precise). Interestingly\, the usual standard axio
 ms of set theory leave open how complex a monstrous set must be: This depe
 nds\, roughly speaking\, on what large cardinals exist in the set theoreti
 cal universe. A classical result of Arnie Miller shows that in the smalles
 t universe (Gödel's constructible universe) there are co-analytic monstrou
 s sets (that is\, they are as simple as they can possibly be\; meaning thi
 s universe is itself somewhat 'monstrous'). In this talk I will discuss a 
 recent joint result with Vera Fischer and Thilo Weinert\, stating that a s
 imilar same conclusion can be proved in a specific\, well-known extension 
 of the axioms of set theory: Namely\, under the Bounded Proper Forcing Axi
 om (BPFA) plus an assumption which limits the size of the large cardinals 
 in our universe (an anti-large cardinal assumption)\, there are Π12 Hamel 
 bases\, mad families\, etc. This is to say\, provided there are almost no 
 large cardinals\, models of BPFA are 'almost as monstrous' as the minimal 
 model of set theory\, Gödel's constructible universe.\n
DTSTART:20190924T183000Z
DTEND:20190924T193000Z
LOCATION:Room 920\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue 
 Sherbrooke Ouest
SUMMARY:David Schrittesser (Vienna)
URL:/mathstat/channels/event/david-schrittesser-vienna
 -300686
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