A note on tall cardinals and level by level equivalence

Starting from a model V “ZFC + GCH + κ is supercompact + No cardinal is supercompact up to a measurable cardinal”, we force and construct a model V P such that V P “ZFC + κ is supercompact + No cardinal is supercompact up to a measurable cardinal + δ is measurable iff δ is tall” in which level by level equivalence between strong compactness and supercompactness holds. This extends and generalizes both [4, Theorem 1] and the results of [5].

• Type: Journal
• Year: 2016
• Where: MLQ
• Authors: Arthur W. Apter
• Keywords: MLQ 2016