Mervyn Tong (University of Leeds) – Higher-arity distality

Many model-theoretic dividing lines, such as NIP, stability, and distality, are naturally defined in terms of binary formulas. One can nonetheless study higher-arity formulas under an NIP/stability/distality assumption, but this often turns out to be too strong. This has led to the development of higher-arity NIP, stability, and distality (which are strict weakenings of the binary versions). Of these, higher-arity distality has received the least treatment, and much more work remains before the theory can be applied. In particular, the theory of strong honest definitions for higher-arity distality is relatively undeveloped. I will survey what is known in the literature and discuss my ongoing work.