Almost disjoint families.
Isomorphism via full groups.
Density of topological full groups.
A weak reducibility lemma.
A reducibility lemma.
A dichotomy theorem for graphs induced by commuting families of Borel injections.
A generalized marker lemma.
The axiom of dependent choice and regular open algebras of Baire spaces.
The dual Schröder-Bernstein theorem and Borel equivalence relations.