BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//wp-events-plugin.com//7.2.3.1//EN
TZID:Europe/Paris
X-WR-TIMEZONE:Europe/Paris
BEGIN:VEVENT
UID:5209@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20240620T110000
DTEND;TZID=Europe/Paris:20240620T123000
DTSTAMP:20240613T130726Z
URL:https://www.i2m.univ-amu.fr/evenements/realizability-models-for-large-
 cardinals/
SUMMARY:Richard Matthews (University of Cambridge): Realizability Models fo
 r Large Cardinals
DESCRIPTION:Richard Matthews: The method of realizability was first develop
 ed by Kleene and is seen as a way\nto extract computational content from m
 athematical proofs via the Curry-Howard\nCorrespondence. The Curry-Howard 
 Correspondence is a way to associate with each\nmathematical proof a compu
 ter program. Then\, from a theorem one can extract\ncomputational content 
 by analysing the programs associated to the proof of the\nstatement. Tradi
 tionally\, this method was restricted to producing models which\nsatisfied
  intuitionistic logic\; however it was later extended by Krivine to\nprodu
 ce models which satisfy full classical logic and even Zermelo-Fraenkel set
 \ntheory with choice (ZFC).\n\nLarge cardinals are an important concept in
  set theory asserting the existence\nof certain infinite sets satisfying a
 dditional properties\, which in general\ncannot be proven to exist from th
 e axioms of ZFC. However\, such sets are known\nto provide significant str
 ucture to the set-theoretic universe\, for example\ngiving the existence o
 f Grothendieck universes and other universes satisfying\nvarious closure p
 roperties. We shall show how to build Krivine style\nrealizability models 
 for various large cardinal properties and present some\ngeneral results ab
 out ordinals and cardinals in these models. This is joint\nwork with Laura
  Fontanella and Guillaume Geoffroy.
CATEGORIES:Séminaire,Logique et Interactions
LOCATION:I2M Luminy - TPR2\, Salle de Séminaire 304-306 (3ème étage)\, 1
 63 Avenue de Luminy\, Marseille\, 13009\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=163 Avenue de Luminy\, Mars
 eille\, 13009\, France;X-APPLE-RADIUS=100;X-TITLE=I2M Luminy - TPR2\, Sall
 e de Séminaire 304-306 (3ème étage):geo:0,0
END:VEVENT
BEGIN:VTIMEZONE
TZID:Europe/Paris
X-LIC-LOCATION:Europe/Paris
BEGIN:DAYLIGHT
DTSTART:20240331T030000
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
TZNAME:CEST
END:DAYLIGHT
END:VTIMEZONE
END:VCALENDAR