Distinguishing types of gaps in 𝒫(ω)/fin

Teruyuki Yorioka

doi:10.2178/jsl/1067620186

Abstract

Supplementing the well known results of Kunen we show that Martin’s Axiom is not sufficient to decide the existence of (ω₁,𝔠)-gaps when (𝔠,𝔠)-gaps exist, that is, it is consistent with ZFC that Martin’s Axiom holds and there are (𝔠,𝔠)-gaps but no (ω₁,𝔠)-gaps.

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Teruyuki Yorioka "Distinguishing types of gaps in 𝒫(ω)/fin," Journal of Symbolic Logic 68(4), 1261-1276, (December 2003). https://doi.org/10.2178/jsl/1067620186

Published: December 2003

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