  Our concern is the axiomatisation problem for modal and algebraic logics that
correspond to various fragments of two-variable first-order logic with counting
quantifiers. In particular, we consider modal products with Diff, the
propositional unimodal logic of the difference operator. We show that the
two-dimensional product logic Diff x Diff is non-finitely axiomatisable, but
can be axiomatised by infinitely many Sahlqvist axioms. We also show that its
`square' version (the modal counterpart of the substitution and equality free
fragment of two-variable first-order logic with counting to two) is
non-finitely axiomatisable over Diff x Diff, but can be axiomatised by adding
infinitely many Sahlqvist axioms. These are the first examples of products of
finitely axiomatisable modal logics that are not finitely axiomatisable, but
axiomatisable by explicit infinite sets of canonical axioms.
