Mathematical Research Letters

Volume 9 (2002)

Number 5

Duality and the pcf theory

Pages: 585 – 595



Saharon Shelah (Hebrew University)

Jindrich Zapletal (University of Florida)


We consider natural cardinal invariants $\hm_{\it n}$ and prove several duality theorems, saying roughly: if $I$ is a suitably definable ideal and provably $\cov(I)\geq\hm_{\it n}$, then $\non(I)$ is provably small. The proofs integrate the determinacy theory, forcing and pcf theory.

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