Can an infinite self-dual uniform matroid be constructed in ZFC?

The manuscript constructs, in ZFC, a self-dual uniform matroid $Q$ on a countable set with every basis and its complement infinite, answering the Bowler-Geschke question and the Gollin-Joo existence question affirmatively. Its bases satisfy an extra ordinal inequality used to build the packing/covering counterexample. It does not address uncountable ground sets or classify such matroids.

The manuscript constructs, in ZFC, a self-dual uniform matroid $Q$ on a countable set with every basis and its complement infinite, answering the Bowler-Geschke question and the Gollin-Joo existence question affirmatively. Its bases satisfy an extra ordinal inequality used to build the packing/covering counterexample. It does not address uncountable ground sets or classify such matroids.