The Hart-Shelah example, in stronger logics

We generalize the Hart-Shelah example \cite{HaSh:323} to higher infinitary logics. We build, for each natural number k\geq 2 and for each infinite cardinal \lambda, a sentence \psi_k^\lambda of the logic L_{(2^\lambda)^+,\omega} that (modulo mild set theoretical hypotheses around \lambda and assuming 2^\lambda < \lambda^{+m}) is categorical in \lambda^+,\dots,\lambda^{+k-1} but not... Show more