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UID:/NewsandEvents/Archives/2015/newsitem/7045/18-
 November-2015-Algebra|Coalgebra-Seminar-Alberto-Ga
 tto
DTSTAMP:20151108T000000
SUMMARY:Algebra|Coalgebra Seminar, Alberto Gatto
ATTENDEE;ROLE=Speaker:Alberto Gatto
DTSTART;TZID=Europe/Amsterdam:20151118T171500
DTEND;TZID=Europe/Amsterdam:20151118T181500
LOCATION:Room F3.20, Science Park 107, Amsterdam
DESCRIPTION:I will introduce the first-order langu
 ages L2 and Lt (from 'Topological model theory' by
  Flum and Ziegler), and the modal language Lm with
  derivative and counting operators. I will then il
 lustrate original work which establishes the equiv
 alence between Lt and Lm over T3 spaces, and that 
 the result fails over T2 spaces. I will then prese
 nt a recent axiomatisation of the Lm theory of the
  classes of all T3, T2, and T1 spaces. I will then
  discuss the open problem of proving that Lm enric
 hed with only finitely many other modal operators 
 is still less expressive than Lt over T2 spaces, a
 nd present some partial results. Finally, I will c
 onclude by illustrating possible directions of fut
 ure work.  For more information, see https://www.i
 llc.uva.nl/alg-coalg or contact Frederik Lauridsen
  (f.m.lauridsen at uva.nl) or Julia Ilin (ilin.jul
 i at gmail.com).
X-ALT-DESC;FMTTYPE=text/html:\n        <p>I will i
 ntroduce the first-order languages L2 and Lt (from
  'Topological model theory' by Flum and Ziegler), 
 and the modal language Lm with derivative and coun
 ting operators. I will then illustrate original wo
 rk which establishes the equivalence between Lt an
 d Lm over T3 spaces, and that the result fails ove
 r T2 spaces. I will then present a recent axiomati
 sation of the Lm theory of the classes of all T3, 
 T2, and T1 spaces. I will then discuss the open pr
 oblem of proving that Lm enriched with only finite
 ly many other modal operators is still less expres
 sive than Lt over T2 spaces, and present some part
 ial results. Finally, I will conclude by illustrat
 ing possible directions of future work.</p>\n    \
 n        <p>For more information, see <a target="_
 blank" href="https://www.illc.uva.nl/alg-coalg">ht
 tps://www.illc.uva.nl/alg-coalg</a> or contact Fre
 derik Lauridsen (<a class="email">f.m.lauridsen <s
 pan class="at">at</span> uva.nl</a>) or Julia Ilin
  (<a class="email">ilin.juli <span class="at">at</
 span> gmail.com</a>).</p>\n    
URL:/NewsandEvents/Archives/2015/newsitem/7045/18-
 November-2015-Algebra|Coalgebra-Seminar-Alberto-Ga
 tto
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