Alberto Marcone will be visiting Swansea for a few days! He’s arriving tomorrow evening and will stay here for the whole next week. So this is a perfect chance to kick-off the theory seminar for the second semester. Please find the title and abstract of his talk below. We will meet in the theory lab on Thursday 22 Jan, 4pm.

Title: The reverse mathematics of dimension of posets

Abstract: In 1941 Dushnik and Miller defined the dimension of a poset: the minimum number of linear extensions of the poset whose intersection is exactly the poset itself. We study the reverse mathematics of some theorems that bound the increase in the dimension of a poset when we extend it adding new points or chains. Some results turn out to be equivalent to WKL_0, but one can be proved either by a compactness argument or using extra induction: we haven’t pinpointed its exact strength yet, but we have some preliminary results.

This project was started a few years ago in collaboration with Marta Fiori Carones and recently revamped jointly with Andrea Volpi.