The failure of square at all uncountable cardinals is…
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The failure of square at all uncountable cardinals is weaker than a Woodin limit of Woodin cardinals
arXiv:2602.13077 \math.LO\]: [https://arxiv.org/abs/2602.13077 https://arxiv.org/abs/2602.13077
Douglas Blue, Paul Larson, Grigor Sargsyan
Abstract: "We force the Axiom of Choice over the least initial segment of a Nairian model satisfying ZF. In the forcing extension, square\_kappa fails at all uncountable cardinals kappa, and every regular cardinal is omega-strongly measurable in HOD, as witnessed by the omega-club filter. Thus the failure of square everywhere is within the current reach of inner model theory, and the HOD Hypothesis is not provable in ZFC."
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arXiv:2602.13077 \math.LO\]: [https://arxiv.org/abs/2602.13077 https://arxiv.org/abs/2602.13077
Douglas Blue, Paul Larson, Grigor Sargsyan
Abstract: "We force the Axiom of Choice over the least initial segment of a Nairian model satisfying ZF. In the forcing extension, square\_kappa fails at all uncountable cardinals kappa, and every regular cardinal is omega-strongly measurable in HOD, as witnessed by the omega-club filter. Thus the failure of square everywhere is within the current reach of inner model theory, and the HOD Hypothesis is not provable in ZFC."
#science
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