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UID:/NewsandEvents/Archives/2020/newsitem/11553/19
-February-2020-Algebra|Coalgebra-Seminar-Iris-van-
der-Giessen
DTSTAMP:20200211T134507
SUMMARY:Algebra|Coalgebra Seminar, Iris van der Gi
essen
ATTENDEE;ROLE=Speaker:Iris van der Giessen
DTSTART;TZID=Europe/Amsterdam:20200219T160000
DTEND;TZID=Europe/Amsterdam:20200219T170000
LOCATION:ILLC Seminar Room F1.15, Science Park 107
, Amsterdam
DESCRIPTION:Abstract: I would like to present ong
oing work on intuitionistic modal logics iGL and i
SL which have a close connection to the (unknown!)
provability logic of Heyting Arithmetic. Classica
lly, Gödel-Löb logic GL admits a provability inter
pretation for Peano Arithmetic. iGL is its intuiti
onistic counterpart and iSL is iGL extended by exp
licit completeness principles. I will characterize
both systems via an axiomatization and in terms o
f Kripke models. The main goal is to understand th
eir admissible rules in order to get insight in th
e structure of those logics. To do so, I want to f
ocus on one step in this direction: Ghilardi’s won
derful result connecting projective formulas to th
e extension property in Kripke models.
X-ALT-DESC;FMTTYPE=text/html:\n Abstract:

\
n I would like to present ongoing work on intuiti
onistic modal logics iGL and iSL which have a clos
e connection to the (unknown!) provability logic o
f Heyting Arithmetic. Classically, Gödel-Löb logic
GL admits a provability interpretation for Peano
Arithmetic. iGL is its intuitionistic counterpart
and iSL is iGL extended by explicit completeness p
rinciples. I will characterize both systems via an
axiomatization and in terms of Kripke models. The
main goal is to understand their admissible rules
in order to get insight in the structure of those
logics. To do so, I want to focus on one step in
this direction: Ghilardi’s wonderful result connec
ting projective formulas to the extension property
in Kripke models.

URL:http://events.illc.uva.nl/alg-coalg/
CONTACT:Jan Rooduijn at j.m.w.rooduijn at uva.nl
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