On Some Infinitary Logics

Jouko Vaananen, Boban Velickovic

We define a new class of infinitary logics ${\mathcal{L}}_{\kappa ,\alpha }^1$ generalizing Shelah's logic ${\mathbb{L}}_{\kappa }^1$ defined in \cite{MR2869022}. If $\kappa ={\beth }_{\kappa }$ and $\alpha <\kappa$ is infinite then o…