18 November 2015, Algebra|Coalgebra Seminar, Alberto Gatto

I will introduce the first-order languages L2 and Lt (from 'Topological model theory' by Flum and Ziegler), and the modal language Lm with derivative and counting operators. I will then illustrate original work which establishes the equivalence between Lt and Lm over T3 spaces, and that the result fails over T2 spaces. I will then present 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 enriched with only finitely many other modal operators is still less expressive than Lt over T2 spaces, and present some partial results. Finally, I will conclude by illustrating possible directions of future work.

For more information, see http://www.illc.uva.nl/alg-coalg or contact Frederik Lauridsen (f.m.lauridsen at uva.nl) or Julia Ilin (ilin.juli at gmail.com).