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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

### Keywords

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

# 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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