The distributivity numbers of finite products of P(omega) /fin

1998/01/15 by Saharon Shelah, Shelah, Saharon, Otmar Spinas +1
Mathematics · Computer Science · #Advanced Topology and Set Theory #Limits and Structures in Graph Theory #Computability, Logic, AI Algorithms

paper · pdf · doi:10.48550/arxiv.math/9801151

Abstract

Generalizing [ShSi:494], for every n< omega we construct a ZFC-model where the distributivity number of r.o. (P(omega)/fin)ⁿ⁺¹, h(n+1), is smaller than the one of r.o.(P(omega)/fin)ⁿ. This answers an old problem of Balcar, Pelant and Simon. We also show that Laver and Miller forcing collapse the continuum to h(n) for every n

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