### Archives

### 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

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

# Tag Archives: Singular coﬁnality

## 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
Leave a comment