This post is about the paper Reverse Mathematics of Matroids by Jeff Hirst and me. We look at basis theorems for countable vector spaces, countable graphs, and countable enumerated matroids. These three kinds of structures turn out to be extremely similar from the point of view of their dependence relations.

### Boole’s Rings

- The reflection principle $R_2$ May 20, 2016 Assaf Rinot
- The pirate treasure division problem May 20, 2016 Joel David Hamkins
- Generic Vopěnka’s Principle at YST2016 May 17, 2016 Victoria Gitman
- How does a slinky fall? May 10, 2016 Joel David Hamkins
- Jacob Davis, PhD 2016, Carnegie Mellon University May 2, 2016 Joel David Hamkins

### Comments on Boole’s Rings

- Comment on A relative of the approachability ideal, diamond and non-saturation by saf May 20, 2016 Comments for Assaf Rinot
- Comment on A relative of the approachability ideal, diamond and non-saturation by The reflection principle $R_2$ | Assaf Rinot May 20, 2016 Comments for Assaf Rinot
- Comment on Square principles by The reflection principle $R_2$ | Assaf Rinot May 20, 2016 Comments for Assaf Rinot
- Comment on Chain conditions of products, and weakly compact cardinals by The reflection principle $R_2$ | Assaf Rinot May 20, 2016 Comments for Assaf Rinot
- Comment on A Microscopic approach to Souslin-tree constructions. Part I by Square principles | Assaf Rinot May 19, 2016 Comments for Assaf Rinot