The least weakly compact cardinal can be unfoldable, weakly measurable and nearly $${\theta}$$θ-supercompact

We prove from suitable large cardinal hypotheses that the least weakly compact cardinal can be unfoldable, weakly measurable and even nearly $${\theta}$$θ-supercompact, for any desired $${\theta}$$θ. In addition, we prove several global results showing how the entire class of weakly compactcardinals, a proper class, can be made to coincide with the class of unfoldable cardinals, with the class of weakly measurable cardinals or with the class of nearly $${\theta_\kappa}$$θκ-supercompact cardinals $${\kappa}$$κ, for nearly any desired function $${\kappa\mapsto\theta_\kappa}$$κ↦θκ. These results answer several questions that had been open in the literature and extend to these large cardinals the identity-crises phenomenon, first identified by Magidor with the strongly compact cardinals.

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