Algebra seminar - February 13, 1pm, lecture room M5 Print

We will continue on Thursday, February 13, in M5 at 1pm by the talk

F. Pakhomov

Dilators and Ptykes

Dilators are endofunctors D:WO->WO preserving pullbacks and directed co-limits, where WO is the category of well-orderings and strictly monotone maps. This notion was introduced by J.-Y. Girard as one of central notions within his approach to certain problems in proof-theory (calculation of proof-theoretic ordinals). Some more sophisticated applications motivate higher-order generalizations of the notion of dilator, known as ptykes. For example, ptykes of the type (WO->WO)->WO are functors from the category of dilators Dil to WO that preserve pullbacks  and  directed co-limits (here Dil is the category of dilators and Cartesian natural transformations).

In the first part of the talk I plan to discuss dilators, some basic results about them, and give some idea about their applications in proof-theory.  Next I plan to talk about my approach to the theory of ptykes, where  types of ptykes are interpreted as classes of relational structures that are closed under substructures.

Last Updated on Thursday, 06 February 2020 16:13