Hanf Number for Scott Sentences of Computable Structures

Sergey Goncharov, Julia Knight, Ioannis Souldatos

The Hanf number for a set $S$ of sentences in $L_{{\omega }_1,\omega }$ (or some other logic) is the least infinite cardinal $\kappa$ such that for all $\phi \in S$, if $\phi$ has models in all infinite car…