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.
J. Symbolic Logic
68(4):
1261-1276
(December 2003).
DOI: 10.2178/jsl/1067620186
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