The unrestricted infinite matroid intersection and packing/covering conjectures

Theorem 1.1: in ZFC there are a countably infinite set $E$ and two self-dual infinite matroids $M_0,M_1$ on $E$ with $I_0\cup I_1\ne E$ for all independent $I_0,I_1$; the pair has no packing/covering partition, so the infinite matroid packing/covering conjecture is false. Corollary 1.2: the same partitional pair fails intersection, refuting the unrestricted infinite Matroid Intersection Conjecture and answering Joo's Question 1.5 negatively. The examples are neither finitary nor cofinitary, so Nash-Williams' original conjecture for finitary matroids and the cofinitary cases are untouched. The local building block also answers the Bowler-Geschke ZFC question on self-dual uniform matroids (separate entry).

Theorem 1.1: in ZFC there are a countably infinite set $E$ and two self-dual infinite matroids $M_0,M_1$ on $E$ with $I_0\cup I_1\ne E$ for all independent $I_0,I_1$; the pair has no packing/covering partition, so the infinite matroid packing/covering conjecture is false. Corollary 1.2: the same partitional pair fails intersection, refuting the unrestricted infinite Matroid Intersection Conjecture and answering Joo's Question 1.5 negatively. The examples are neither finitary nor cofinitary, so Nash-Williams' original conjecture for finitary matroids and the cofinitary cases are untouched. The local building block also answers the Bowler-Geschke ZFC question on self-dual uniform matroids (separate entry).