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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

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

# 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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