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Combinatorial dichotomies and cardinal invariants

Combinatorial dichotomies and cardinal invariants

Assuming the P-ideal dichotomy, we attempt to isolate those cardinal characteristics of the continuum that are correlated with two well-known consequences of the proper forcing axiom.We find a cardinal invariant x such that the statement that x > ω 1 is equivalent to the statement that 1, ω, ω 1 …