Level by level inequivalence beyond measurability

Level by Level Inequivalence , Strong Compactness , and GCH ∗ † Arthur

We construct three models containing exactly one supercompact cardinal in which level by level inequivalence between strong compactness and supercompactness holds. In the first two models, below the supercompact cardinal κ, there is a non-supercompact strongly compact cardinal. In the last model, any suitably defined ground model Easton function is realized.

On the consistency strength of level by level inequivalence

We show that the theories “ZFC + There is a supercompact cardinal” and “ZFC + There is a supercompact cardinal + Level by level inequivalence between strong compactness and supercompactness holds” are equiconsistent.

Tallness and level by level equivalence and inequivalence

We construct two models containing exactly one supercompact cardinal in which all nonsupercompact measurable cardinals are strictly taller than they are either strongly compact or supercompact. In the first of these models, level by level equivalence between strong compactness and supercompactness holds. In the other, level by level inequivalence between strong compactness and supercompactness ...

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Indestructibility, instances of strong compactness, and level by level inequivalence

Suppose λ > κ is measurable. We show that if κ is either indestructibly supercompact or indestructibly strong, then A = {δ < κ | δ is measurable, yet δ is neither δ+ strongly compact nor a limit of measurable cardinals} must be unbounded in κ. The large cardinal hypothesis on λ is necessary, as we further demonstrate by constructing via forcing two models in which A = ∅. The first of these cont...