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### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- 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

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

# 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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