On the consistency strength of the Milner–Sauer conjecture

Annals of Pure and Applied Logic 140 (1):110-119 (2006)
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Abstract

In their paper from 1981, Milner and Sauer conjectured that for any poset P,≤, if , then P must contain an antichain of cardinality κ. The conjecture is consistent and known to follow from GCH-type assumptions. We prove that the conjecture has large cardinals consistency strength in the sense that its negation implies, for example, the existence of a measurable cardinal in an inner model. We also prove that the conjecture follows from Martin’s Maximum and holds for all singular λ above the first strongly compact cardinal

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10.1016/j.apal.2005.09.012

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Citations of this work

On cardinal characteristics of Yorioka ideals.Miguel A. Cardona & Diego A. Mejía - 2019 - Mathematical Logic Quarterly 65 (2):170-199.
On the consistency strength of the Milner–Sauer conjecture.Assaf Rinot - 2006 - Annals of Pure and Applied Logic 140 (1):110-119.
Antichains in partially ordered sets of singular cofinality.Assaf Rinot - 2007 - Archive for Mathematical Logic 46 (5-6):457-464.

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References found in this work

The core model.A. Dodd & R. Jensen - 1981 - Annals of Mathematical Logic 20 (1):43-75.
The covering lemma for K.Tony Dodd & Ronald Jensen - 1982 - Annals of Mathematical Logic 22 (1):1-30.
The strenght of the failure of the singular cardinal hypothesis.Moti Gitik - 1991 - Annals of Pure and Applied Logic 51 (3):215-240.
On the consistency strength of the Milner–Sauer conjecture.Assaf Rinot - 2006 - Annals of Pure and Applied Logic 140 (1):110-119.
Strong compactness and other cardinal sins.Jussi Ketonen - 1972 - Annals of Mathematical Logic 5 (1):47.

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