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### Recent blog posts

- 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

### Keywords

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

# Tag Archives: Poset

## 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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