The Hart-Shelah example, in strong logics

by Shelah and Villaveces. [ShVi:648]

We build an example that generalizes [HaSh:323] to uncountable cases. In particular, our example yields a sentence psi in L_{(2^lambda)^+, omega} that is categorical in lambda, lambda^+, ..., lambda^{+k} but not in beth_{k+1}(lambda)^+ . This is connected with the L os Conjecture and with Shelah's own conjecture and construction of excellent classes for the psi in L_{omega_1, omega} case.

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