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.