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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Completeness of infinitary intuitionistic logics -
Espindola\, CR (Stockholm University)
DTSTART;TZID=Europe/London:20150825T133000
DTEND;TZID=Europe/London:20150825T140000
UID:TALK60452AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/60452
DESCRIPTION:Completeness theorems for infinitary classical log
ics have been known for decades. When removing the
law of excluded middle\, however\, the situation
is more difficult to analyse even in the propositi
onal case\, as the main obstacle for studying infi
nitary intuitionistic logics is the huge variety o
f non-equivalent formulas that one can obtain. Com
pleteness results for the propositional fragment a
nd disjunctions and conjunctions of countable size
have been obtained\, but the general case has not
been addressed. The purpose of this talk is to ou
tline set-theoretical and category-theoretical tec
hniques that allow the study of completeness theor
ems for infinitary intuitionistic logics in the ge
neral case\, both for propositional and first-orde
r logics\, in terms of an infinitary Kripke semant
ics. We will also analyse to what extent\n the use
of large cardinal axioms (more precisely\, weakly
compact cardinals) is necessary\, and some applic
ations of these completeness results will be prese
nted.\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
CONTACT:
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