The talk is about the normal modal logics of elementary classes defined by first-order formulas of the form
'for all x_0 there exist x_1, ..., x_n phi(x_0, x_1, ... x_n)' with phi being a conjunction of binary atoms.
I'll show that many properties of these logics, such as finite axiomatisability,
elementarity, axiomatisability by a set of canonical formulas or by a single generalised Sahlqvist formula,
together with modal definability of the initial formula, either simultaneously hold or simultaneously do not hold.
- Logic Seminar