THE LEAST WEAKLY COMPACT CARDINAL CAN BE UNFOLDABLE, WEAKLY MEASURABLE AND NEARLY θ-SUPERCOMPACT

Abstract. We provefrom suitable largecardinalhypothesesthat the least weakly compact cardinal can be unfoldable, weakly measurable and even nearly θ-supercompact, for any desired θ. In addition, we prove several global results showing how the entire class of weakly compact cardinals, 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 θκ-supercompact cardinals κ, for nearly any desired function κ ↦ → θκ. These results answer several questions that had been open in the literature andextend tothese largecardinalstheidentity-crisesphenomenon, first identified by Magidor with the strongly compact cardinals. 1