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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

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

# 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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