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

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
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1016/j.apal.2005.09.012
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 71,290
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

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.
External Cofinalities and the Antichain Condition in Partial Orders.Isaac Gorelic - 2006 - Annals of Pure and Applied Logic 140 (1):104-109.

View all 6 references / Add more references

Citations of this work BETA

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.

Add more citations

Similar books and articles

Consistency Strength of Higher Chang’s Conjecture, Without CH.Sean D. Cox - 2011 - Archive for Mathematical Logic 50 (7-8):759-775.
Antichains in Partially Ordered Sets of Singular Cofinality.Assaf Rinot - 2007 - Archive for Mathematical Logic 46 (5-6):457-464.
The Consistency Strength of an Infinitary Ramsey Property.George Kafkoulis - 1994 - Journal of Symbolic Logic 59 (4):1158-1195.
Chang’s Conjecture and Weak Square.Hiroshi Sakai - 2013 - Archive for Mathematical Logic 52 (1-2):29-45.
On the Consistency Strength of Two Choiceless Cardinal Patterns.Arthur W. Apter - 1999 - Notre Dame Journal of Formal Logic 40 (3):341-345.
A Remark on the Tree Property in a Choiceless Context.Arthur W. Apter - 2011 - Archive for Mathematical Logic 50 (5-6):585-590.
Mr. Sauer Replies.James L. Sauer - 1986 - The Chesterton Review 12 (3):413-416.
Borel's Conjecture in Topological Groups.Fred Galvin & Marion Scheepers - 2013 - Journal of Symbolic Logic 78 (1):168-184.

Analytics

Added to PP index
2013-12-31

Total views
9 ( #954,515 of 2,518,732 )

Recent downloads (6 months)
1 ( #408,070 of 2,518,732 )

How can I increase my downloads?

Downloads

My notes