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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

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

# 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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