The nine-frame Fine–Jankov conjecture for ${\sf L}_3$

Let ${\sf L}_3$ be the logic associated with $\beta(\omega^3)$, and let ${\sf S4.1}$ be the base logic. The Fine–Jankov formula of a finite frame is the characteristic formula used to axiomatize the corresponding frame logic. Fine–Jankov conjecture. The logic ${\sf L}_3$ is axiomatizable over ${\sf S4.1}$ by the Fine–Jankov formulas of the nine frames displayed in the source. This is presented as a conjectural step toward axiomatizing ${\sf L}_3$; the paper does not establish it.