Sergey Goncharov, Julia Knight, Ioannis Souldatos
Published 2016-02-02Version 1
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 $\varphi\in S$, if $\varphi$ has models in all infinite cardinalities less than $\kappa$, then it has models of all infinite cardinalities. S-D. Friedman asked what is the Hanf number for Scott sentences of computable structures. We show that the value is $\beth_{\omega_1^{CK}}$.
Hanf number for the strictly stable cases
Some new computable structures of high rank
The Hanf numbers of stationary logic. II. Comparison with other logics
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