We will continue on Thursday, February 13, in M5 at 1pm by the talk
F. Pakhomov
Dilators and Ptykes
Abstract: Dilators are endofunctors D:WO>WO preserving pullbacks and directed colimits, where WO is the category of wellorderings and strictly monotone maps. This notion was introduced by J.Y. Girard as one of central notions within his approach to certain problems in prooftheory (calculation of prooftheoretic ordinals). Some more sophisticated applications motivate higherorder 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 colimits (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 prooftheory. 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.
