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- Prikry forcing may add a Souslin tree June 12, 2016
- The reflection principle $R_2$ May 20, 2016
- Prolific Souslin trees March 17, 2016
- Generalizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
- Happy new jewish year! September 24, 2014
- Square principles April 19, 2014
- Partitioning the club guessing January 22, 2014

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Ostaszewski square Erdos-Hajnal graphs stationary reflection Aronszajn tree P-Ideal Dichotomy Prevalent singular cardinals Almost-disjoint famiy Fast club Cohen real Erdos Cardinal tensor product graph Diamond Sakurai's Bell inequality Poset Rado's conjecture incompactness Forcing Microscopic Approach Fodor-type reflection 05D10 Uniformly coherent Club Guessing Absoluteness polarized partition relation Cardinal Invariants Successor of Singular Cardinal Nonspecial tree weak square coloring number Stevo Todorcevic Martin's Axiom Successor of Regular Cardinal Partition Relations Non-saturation Ascent Path diamond star Postprocessing function Chang's conjecture Generalized Clubs Singular cardinals combinatorics square Minimal Walks Constructible Universe projective Boolean algebra OCA Universal Sequences S-Space Mandelbrot set Reduced Power Hereditarily Lindelöf space Almost countably chromatic Whitehead Problem b-scale Singular coﬁnality L-space Parameterized proxy principle middle diamond Prikry-type forcing Weakly compact cardinal Large Cardinals Distributive tree Kurepa Hypothesis PFA 05A17 Small forcing Foundations Rainbow sets free Boolean algebra Square-Brackets Partition Relations Forcing Axioms Hedetniemi's conjecture approachability ideal Hindman's Theorem Shelah's Strong Hypothesis square principles Cardinal function 20M14 stationary hitting Almost Souslin PFA(S)[S] Fat stationary set Selective Ultrafilter weak diamond Rock n' Roll sap xbox Knaster very good scale Coherent tree Axiom R Uniformization Slim tree Dushnik-Miller Jonsson cardinal reflection principles 11P99 Singular Density HOD ccc Antichain Commutative cancellative semigroups Souslin Tree Chromatic number

# Tag Archives: Singular coﬁnality

## Logic in Hungary, August 2005

These are the slides of a contributed talk given at the Logic in Hungary 2005 meeting (Budapest, 5–11 August 2005). Talk Title: On the consistency strength of the Milner-Sauer Conjecture Abstract: In their paper from 1981, after learning about Pouzet‘s theorem that any … Continue reading

Posted in Contributed Talks
Tagged Antichain, Shelah's Strong Hypothesis, Singular coﬁnality
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## On the consistency strength of the Milner-Sauer conjecture

Abstract: In their paper from 1981, Milner and Sauer conjectured that for any poset $\mathbb P$, if $\text{cf}(\mathbb P)$ is a singular cardinal $\lambda$, then $\mathbb P$ must contain an antichain of size $\text{cf}(\lambda)$. The conjecture is consistent and known … Continue reading

## Antichains in partially ordered sets of singular cofinality

Abstract: In their paper from 1981, Milner and Sauer conjectured that for any poset $\mathbb P$, if $\text{cf}(\mathbb P)$ is a singular cardinal $\lambda$, then $\mathbb P$ must contain an antichain of size $\text{cf}(\lambda)$. The main result of of this … Continue reading

Posted in Publications, Singular Cardinals Combinatorics
Tagged 03E04, 03E35, 06A07, Antichain, Poset, Singular coﬁnality
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