Combinatorial characterization of $\Pi^11$ -indescribability in $P{\kappa}\lambda$

Archive for Mathematical Logic 37 (4):261-272 (1998)

It is proved that $\Pi^1_1$ -indescribability in $P_{\kappa}\lambda$ can be characterized by combinatorial properties without taking care of cofinality of $\lambda$ . We extend Carr's theorem proving that the hypothesis $\kappa$ is $2^{\lambda^{<\kappa}}$ -Shelah is rather stronger than $\kappa$ is $\lambda$ -supercompact
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DOI 10.1007/s001530050097
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