Resolvability in c.c.c. generic extensions

2017/02/01 by Soukup, Lajos, Stanley, Adrienne
#03E35 #54A25 #54A35 #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO)

paper · doi:10.48550/arxiv.1702.00326

Abstract

Every crowded space X is ω-resolvable in the c.c.c generic extension V^Fn(|X|,2) of the ground model. We investigate what we can say about λ-resolvability in c.c.c-generic extensions for λ>ω? A topological space is "monotonically ω₁-resolvable" if there is a function f:X→ ω₁ such that \x∈ X: f(x)≥ α \⊂^denseX for each α

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