Chain Logic and Shelah's Infinitary Logic

Mirna Džamonja, Jouko Väänänen

For a cardinal of the form $\kappa ={\beth }_{\kappa }$, Shelah's logic $L_{\kappa }^1$ has a characterisation as the maximal logic above ${\bigcup }_{\lambda <\kappa }{L}_{\lambda ,\omega }$ satisfying Strong Undefinability of Well O…