Tue, 27 Oct 2026, 1:25 pm MDT
Distalty is a model-theoretic tameness-notion, which generalizes o-minimality and strengthens NIP,
containing important unstable theories such as DLO, real closed fields and
Presburger arithmetic. Its consequences include the strong Erdős–Hajnal property.
One interesting problem is that of preserving tameness when adding new predicates or
functions. I will discuss some results around this problem from existing literature and some
from my master’s thesis and from ongoing joint work with Alessio Mansutti and Michael
Benedikt, all concerning distal expansions of Presburger arithmetic and RCF by functions
and by additional relations on distinguished subsets. These include distality of Semënov
arithmetic—the natural numbers with addition, order and the function n -> 2^n —and the
corresponding expansions by the Fibonacci sequence, the Factorial function and other
fast-growing functions.
[video]